Relevant bibliographies by topics / Discontinous Galerkin method

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Discontinous Galerkin method'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Discontinous Galerkin method.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Discontinous Galerkin method"

1

Krasnov, Mikhail Mikhailovich, Marina Eugenievna Ladonkina, and Vladimir Fedorovich Tishkin. "Implementation of the Galerkin discontinous method in the DGM software package." Keldysh Institute Preprints, no. 245 (2018): 1–31. http://dx.doi.org/10.20948/prepr-2018-245.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Dolejší, V., M. Feistauer, and C. Schwab. "On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow." Mathematica Bohemica 127, no. 2 (2002): 163–79. http://dx.doi.org/10.21136/mb.2002.134171.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Cockburn, B. "Discontinuous Galerkin methods." ZAMM 83, no. 11 (November 3, 2003): 731–54. http://dx.doi.org/10.1002/zamm.200310088.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Krasnov, M. M., P. A. Kuchugov, M. E. Ladonkina, and V. F. Tishkin. "Efficient parallel software system for solving Navier-Stokes equations by the discontinuous Galerkin method." Computational Mathematics and Information Technologies 2 (2017): 148–55. http://dx.doi.org/10.23947/2587-8999-2017-2-148-155.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Zhang, Xu-jiu, Yong-sheng Zhu, Ke Yan, and You-yun Zhang. "A Front Tracking Method Based on Runge-Kutta Discontinuous Galerkin Methods." International Journal of Online Engineering (iJOE) 12, no. 12 (December 25, 2016): 67. http://dx.doi.org/10.3991/ijoe.v12i12.6453.

Full text
Abstract:
In this paper, a high-resolution front tracking method was presented for interface tracking simulation with Runge-Kutta discontinuous Galerkin methods. An interface treating method of the discontinuous methods is presented. This method don’t construct the ghost fluid and the flow information on both sides next to the interface is used to solve the interfacial status. The limiter adopted the combination of the shock detection and monotonicity-preserving limiter and level set method is used for tracking the interface. Result shown that the front tracking of the high-order accurate Runge-Kutta discontinuous Galerkin method exhibits very good agreement with exact solution in the interface condition that contain strong shock.
APA, Harvard, Vancouver, ISO, and other styles
6

Xu, Liyang, Xinhai Xu, Xiaoguang Ren, Yunrui Guo, Yongquan Feng, and Xuejun Yang. "Stability evaluation of high-order splitting method for incompressible flow based on discontinuous velocity and continuous pressure." Advances in Mechanical Engineering 11, no. 10 (October 2019): 168781401985558. http://dx.doi.org/10.1177/1687814019855586.

Full text
Abstract:
In this work, we deal with high-order solver for incompressible flow based on velocity correction scheme with discontinuous Galerkin discretized velocity and standard continuous approximated pressure. Recently, small time step instabilities have been reported for pure discontinuous Galerkin method, in which both velocity and pressure are discretized by discontinuous Galerkin. It is interesting to examine these instabilities in the context of mixed discontinuous Galerkin–continuous Galerkin method. By means of numerical investigation, we find that the discontinuous Galerkin–continuous Galerkin method shows great stability at the same configuration. The consistent velocity divergence discretization scheme helps to achieve more accurate results at small time step size. Since the equal order discontinuous Galerkin–continuous Galerkin method does not satisfy inf-sup stability requirement, the instability for high Reynolds number flow is investigated. We numerically demonstrate that fine mesh resolution and high polynomial order are required to obtain a robust system. With these conclusions, discontinuous Galerkin–continuous Galerkin method is able to achieve high-order spatial convergence rate and accurately simulate high Reynolds flow. The solver is tested through a series of classical benchmark problems, and efficiency improvement is proved against pure discontinuous Galerkin scheme.
APA, Harvard, Vancouver, ISO, and other styles
7

Zhang, Rongpei, Xijun Yu, Jiang Zhu, Abimael F. D. Loula, and Xia Cui. "Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation." Communications in Computational Physics 14, no. 5 (November 2013): 1287–303. http://dx.doi.org/10.4208/cicp.190612.010313a.

Full text
Abstract:
AbstractWeighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semi-implicit integration factor method to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.
APA, Harvard, Vancouver, ISO, and other styles
8

Zienkiewicz, O. C., R. L. Taylor, S. J. Sherwin, and J. Peiró. "On discontinuous Galerkin methods." International Journal for Numerical Methods in Engineering 58, no. 8 (August 6, 2003): 1119–48. http://dx.doi.org/10.1002/nme.884.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Hu, Qingjie, Yinnian He, Tingting Li, and Jing Wen. "A Mixed Discontinuous Galerkin Method for the Helmholtz Equation." Mathematical Problems in Engineering 2020 (May 4, 2020): 1–9. http://dx.doi.org/10.1155/2020/9582583.

Full text
Abstract:
In this paper, we introduce and analyze a mixed discontinuous Galerkin method for the Helmholtz equation. The mixed discontinuous Galerkin method is designed by using a discontinuous Pp+1−1−Pp−1 finite element pair for the flux variable and the scattered field with p≥0. We can get optimal order convergence for the flux variable in both Hdiv-like norm and L2 norm and the scattered field in L2 norm numerically. Moreover, we conduct the numerical experiments on the Helmholtz equation with perturbation and the rectangular waveguide, which also demonstrate the good performance of the mixed discontinuous Galerkin method.
APA, Harvard, Vancouver, ISO, and other styles
10

Gopalakrishnan, J., and G. Kanschat. "A multilevel discontinuous Galerkin method." Numerische Mathematik 95, no. 3 (September 1, 2003): 527–50. http://dx.doi.org/10.1007/s002110200392.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Discontinous Galerkin method"

1

Ozisik, Sevtap. "Fully Computable Convergence Analysis Of Discontinous Galerkin Finite Element Approximation With An Arbitrary Number Of Levels Of Hanging Nodes." Phd thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614345/index.pdf.

Full text
Abstract:
In this thesis, we analyze an adaptive discontinuous finite element method for symmetric second order linear elliptic operators. Moreover, we obtain a fully computable convergence analysis on the broken energy seminorm in first order symmetric interior penalty discontin- uous Galerkin finite element approximations of this problem. The method is formulated on nonconforming meshes made of triangular elements with first order polynomial in two di- mension. We use an estimator which is completely free of unknown constants and provide a guaranteed numerical bound on the broken energy norm of the error. This estimator is also shown to provide a lower bound for the broken energy seminorm of the error up to a constant and higher order data oscillation terms. Consequently, the estimator yields fully reliable, quantitative error control along with efficiency. As a second problem, explicit expression for constants of the inverse inequality are given in 1D, 2D and 3D. Increasing mathematical analysis of finite element methods is motivating the inclusion of mesh dependent terms in new classes of methods for a variety of applications. Several inequalities of functional analysis are often employed in convergence proofs. Inverse estimates have been used extensively in the analysis of finite element methods. It is char- acterized as tools for the error analysis and practical design of finite element methods with terms that depend on the mesh parameter. Sharp estimates of the constants of this inequality is provided in this thesis.
APA, Harvard, Vancouver, ISO, and other styles
2

Nytra, Jan. "Řešení problémů akustiky pomocí nespojité Galerkinovy metody." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232174.

Full text
Abstract:
Parciální diferenciální rovnice hrají důležitou v inženýrských aplikacích. Často je možné tyto rovnice řešit pouze přibližně, tj. numericky. Z toho důvodu vzniklo množství diskretizačních metod pro řešení těchto rovnic. Uvedená nespojitá Galerkinova metoda se zdá jako velmi obecná metoda pro řešení těchto rovnic, především pak pro hyperbolické systémy. Naším cílem je řešit úlohy aeroakustiky, přičemž šíření akustických vln je popsáno pomocí linearizovaných Eulerových rovnic. A jelikož se jedná o hyperbolický systém, byla vybrána právě nespojitá Galerkinova metoda. Mezi nejdůležitější aspekty této metody patří schopnost pracovat s geometricky složitými oblastmi, možnost dosáhnout metody vysokého řádu a dále lokální charakter toho schématu umožnuje efektivní paralelizaci výpočtu. Nejprve uvedeme nespojitou Galerkinovu metodu v obecném pojetí pro jedno- a dvoudimenzionalní úlohy. Algoritmus následně otestujeme pro řešení rovnice advekce, která byla zvolena jako modelový případ hyperbolické rovnice. Metoda nakonec bude testována na řadě verifikačních úloh, které byly formulovány pro testování metod pro výpočetní aeroakustiku, včetně oveření okrajových podmínek, které, stejně jako v případě teorie proudění tekutin, jsou nedílnou součástí výpočetní aeroakustiky.
APA, Harvard, Vancouver, ISO, and other styles
3

Bonnasse-Gahot, Marie. "Simulation de la propagation d'ondes élastiques en domaine fréquentiel par des méthodes Galerkine discontinues." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4125/document.

Full text
Abstract:
Le contexte scientifique de cette thèse est l'imagerie sismique dont le but est de reconstituer la structure du sous-sol de la Terre. Comme le forage a un coût assez élevé, l'industrie pétrolière s'intéresse à des méthodes capables de reconstituer les images de la structure terrestre interne avant de le faire. La technique d'imagerie sismique la plus utilisée est la technique de sismique-réflexion qui est basée sur le modèle de l'équation d'ondes. L'imagerie sismique est un problème inverse qui requiert de résoudre un grand nombre de problèmes directs. Dans ce contexte, nous nous intéressons dans cette thèse à la résolution du problème direct en régime harmonique, soit à la résolution des équations d'Helmholtz. L'objectif principal est de proposer et de développer un nouveau type de solveur élément fini (EF) caractérisé par un opérateur discret de taille réduite (comparée à la taille des solveurs déjà existants) sans pour autant altérer la précision de la solution numérique. Nous considérons les méthodes de Galerkine discontinues (DG). Comme les méthodes DG classiques sont plus coûteuses que les méthodes EF continues si l'on considère un même problème à cause d'un grand nombre de degrés de liberté couplés, résultat des approximations discontinues, nous développons une nouvelle classe de méthode DG réduisant ce problème : la méthode DG hybride (HDG). Pour valider l'efficacité de la méthode HDG proposée, nous comparons les résultats obtenus avec ceux obtenus avec une méthode DG basée sur des flux décentrés en 2D. Comme l'industrie pétrolière s'intéresse au traitement de données réelles, nous développons ensuite la méthode HDG pour les équations élastiques d'Helmholtz 3D
The scientific context of this thesis is seismic imaging which aims at recovering the structure of the earth. As the drilling is expensive, the petroleum industry is interested by methods able to reconstruct images of the internal structures of the earth before the drilling. The most used seismic imaging method in petroleum industry is the seismic-reflection technique which uses a wave equation model. Seismic imaging is an inverse problem which requires to solve a large number of forward problems. In this context, we are interested in this thesis in the modeling part, i.e. the resolution of the forward problem, assuming a time-harmonic regime, leading to the so-called Helmholtz equations. The main objective is to propose and develop a new finite element (FE) type solver characterized by a reduced-size discrete operator (as compared to existing such solvers) without hampering the accuracy of the numerical solution. We consider the family of discontinuous Galerkin (DG) methods. However, as classical DG methods are much more expensive than continuous FE methods when considering steady-like problems, because of an increased number of coupled degrees of freedom as a result of the discontinuity of the approximation, we develop a new form of DG method that specifically address this issue: the hybridizable DG (HDG) method. To validate the efficiency of the proposed HDG method, we compare the results that we obtain with those of a classical upwind flux-based DG method in a 2D framework. Then, as petroleum industry is interested in the treatment of real data, we develop the HDG method for the 3D elastic Helmholtz equations
APA, Harvard, Vancouver, ISO, and other styles
4

Galbraith, Marshall C. "A Discontinuous Galerkin Chimera Overset Solver." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Gürkan, Ceren. "Extended hybridizable discontinuous Galerkin method." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/664035.

Full text
Abstract:
This thesis proposes a new numerical technique: the eXtended Hybridizable Discontinuous Galerkin (X-HDG) Method, to efficiently solve problems including moving boundaries and interfaces. It aims to outperform available methods and improve the results by inheriting favored properties of Discontinuous Galerkin (HDG) together with an explicit interface definition. X-HDG combines the Hybridizable HDG method with an eXtended Finite Element (X-FEM) philosophy, with a level set description of the interface, to form an hp convergent, high order unfitted numerical method. HDG outperforms other Discontinuous Galerkin (DG) methods for problems involving self-adjoint operators, due to its hybridization and superconvergence properties. The hybridization process drastically reduces the number of degrees of freedom in the discrete problem, similarly to static condensation in the context of high-order Continuous Galerkin (CG). On other hand, HDG is based on a mixed formulation that, differently to CG or other DG methods, is stable even when all variables (primal unknowns and derivatives) are approximated with polynomials of the same degree k. As a result, convergence of order k+1 in the L2 norm is proved not only for the primal unknown, but also for its derivatives. Therefore, a simple element-by-element postprocess of the derivatives leads to a superconvergent approximation of the primal variables, with convergence of order k+2 in the L2 norm. X-HDG inherits these favored properties of HDG in front of CG and DG methods; moreover, thanks to the level set description of interfaces, costly remeshing is avoided when dealing with moving interfaces. This work demonstrates that X-HDG keeps the optimal and superconvergence of HDG with no need of mesh fitting to the interface. In Chapters 2 and 3, the X-HDG method is derived and implemented to solve the steady-state Laplace equation on a domain where the interface separates a single material from the void and where the interface separates two different materials. The accuracy and the convergence of X-HDG is tested over examples with manufactured solutions and it is shown that X-HDG outperforms the previous proposals by demonstrating high order optimum and super convergence, together with reduced system size thanks to its hybrid nature, without mesh fitting. In Chapters 4 and 5, the X-HDG method is derived and implemented to solve Stokes interface problem for void and bimaterial interfaces. With X-HDG, high order convergence is demonstrated over unfitted meshes for incompressible flow problems. X-HDG for moving interfaces is studied in Chapter 6. A transient Laplace problem is considered, where the time dependent term is discretized using the backward Euler method. A collapsing circle example together with two-phase Stefan problem are analyzed in numerical examples section. It is demonstrated that X-HDG offers high-order optimal convergence for time-dependent problems. Moreover, with Stefan problem, using a polynomial degree k, a more accurate approximation of interface position is demonstrated against X-FEM, thanks to k+1 convergent gradient approximation of X-HDG. Yet again, results obtained by previous proposals are improved.
Esta tesis propone una nueva técnica numérica: eXtended Hybridizable Discontinuous Galerkin (X-HDG), para resolver eficazmente problemas incluyendo fronteras en movimiento e interfaces. Su objetivo es superar las limitaciones de los métodos disponibles y mejorar los resultados, heredando propiedades del método Hybridizable Discontinuous Galerkin method (HDG), junto con una definición de interfaz explícita. X-HDG combina el método HDG con la filosofía de eXtended Finite Element method (X-FEM), con una descripción level-set de la interfaz, para obtener un método numérico hp convergente de orden superior sin ajuste de la malla a la interfaz o frontera. HDG supera a otros métodos de DG para los problemas implícitos con operadores autoadjuntos, debido a sus propiedades de hibridación y superconvergencia. El proceso de hibridación reduce drásticamente el número de grados de libertad en el problema discreto, similar a la condensación estática en el contexto de Continuous Galerkin (CG) de alto orden. Por otro lado, HDG se basa en una formulación mixta que, a diferencia de CG u otros métodos DG, es estable incluso cuando todas las variables (incógnitas primitivas y derivadas) se aproximan con polinomios del mismo grado k. Como resultado, la convergencia de orden k + 1 en la norma L2 se demuestra no sólo para la incógnita primal sino también para sus derivadas. Por lo tanto, un simple post-proceso elemento-a-elemento de las derivadas conduce a una aproximación superconvergente de las variables primales, con convergencia de orden k+2 en la norma L2. X-HDG hereda estas propiedades. Por otro lado, gracias a la descripción level-set de la interfaz, se evita caro remallado tratando las interfaces móviles. Este trabajo demuestra que X-HDG mantiene la convergencia óptima y la superconvergencia de HDG sin la necesidad de ajustar la malla a la interfaz. En los capítulos 2 y 3, se deduce e implementa el método X-HDG para resolver la ecuación de Laplace estacionaria en un dominio donde la interfaz separa un solo material del vacío y donde la interfaz separa dos materiales diferentes. La precisión y convergencia de X-HDG se prueba con ejemplos de soluciones fabricadas y se demuestra que X-HDG supera las propuestas anteriores mostrando convergencia óptima y superconvergencia de alto orden, junto con una reducción del tamaño del sistema gracias a su naturaleza híbrida, pero sin ajuste de la malla. En los capítulos 4 y 5, el método X-HDG se desarrolla e implementa para resolver el problema de interfaz de Stokes para interfaces vacías y bimateriales. Con X-HDG, de nuevo se muestra una convergencia de alto orden en mallas no adaptadas, para problemas de flujo incompresible. X-HDG para interfaces móviles se discute en el Capítulo 6. Se considera un problema térmico transitorio, donde el término dependiente del tiempo es discretizado usando el método de backward Euler. Un ejemplo de una interfaz circulas que se reduce, junto con el problema de Stefan de dos fases, se discute en la sección de ejemplos numéricos. Se demuestra que X-HDG ofrece un alto grado de convergencia óptima para problemas dependientes del tiempo. Además, con el problema de Stefan, usando un grado polinomial k, se demuestra una aproximación más exacta de la posición de la interfaz contra X-FEM, gracias a la aproximación del gradiente convergente k + 1 de X-HDG. Una vez más, se mejoran los resultados obtenidos por las propuestas anteriores
APA, Harvard, Vancouver, ISO, and other styles
6

Elfverson, Daniel. "On discontinuous Galerkin multiscale methods." Licentiate thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-200260.

Full text
Abstract:
In this thesis a new multiscale method, the discontinuous Galerkin multiscale method, is proposed. The method uses localized fine scale computations to correct a global coarse scale equation and thereby takes the fine scale features into account. We show a priori error bounds for convection dominated diffusion-convection-reaction problems with variable coefficients. We also present a posteriori error bound in the case of no convection or reaction and present an adaptive algorithm which tunes the method parameters automatically. We also present extensive numerical experiments which verify our analytical findings.
APA, Harvard, Vancouver, ISO, and other styles
7

Voonna, Kiran. "Development of discontinuous galerkin method for 1-D inviscid burgers equation." ScholarWorks@UNO, 2003. http://louisdl.louislibraries.org/u?/NOD,75.

Full text
Abstract:
Thesis (M.S.)--University of New Orleans, 2003.
Title from electronic submission form. "A thesis ... in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical Engineering"--Thesis t.p. Vita. Includes bibliographical references.
APA, Harvard, Vancouver, ISO, and other styles
8

Casoni, Rero Eva. "Shock capturing for discontinuous Galerkin methods." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/51571.

Full text
Abstract:
Aquesta tesi doctoral proposa formulacions de Galerkin Discontinu (DG) d’alt ordre per la captura de shocks, obtenint alhora solucions altament precises per problemes de flux compressible. En les últimes dècades, la investigació en els mètodes de DG ha estat en constant creixement. L'èxit dels mètodes DG en problemes hiperbòlics ha conduit el seu desenvolupament en lleis de conservació no lineals i problemes de convecció dominant. Entre els avantatges dels mètodes DG, destaquen la seva estabilitat inherent i les propietats locals de conservació. D'altra banda, els mètodes DG estan especialment dissenyats per l’ús aproximacions d'ordre superior. De fet, en els últims anys s'ha demostrat que la resolució de problemes de convecció dominant ja no es restringeix només a elements d'ordre inferior. De fet, es necessiten models numèrics d'alta precisió per aconseguir prediccions altament fiables dins la dinàmica de fluids computacional (CFD). En aquest context es presenten i discuteixen dos tècniques de captura de shocks. En primer lloc, es presenta una tècnica novedosa i senzilla basada en la introducció d'una nova base de funcions de forma. Aquesta base té la capacitat de canviar a nivell local entre una interpolació contínua o discontínua, depenent de la suavitat de la funció que es vol aproximar. En presència de xocs, les discontinuïtats introduïdes dins l’element permeten incloure l'estabilització necessària gràcies a l’ús dels fluxos numèrics, i alhora exploten les propietats intrínsiques del mètodes DG. En conseqüència, es poden utilitzar malles grolleres amb elements d’ordre superior. Amb aquestes discretitzacions i, utilitzant el mètode proposats, els xocs queden continguts a l’interior de l’element i per tant, és possible evitar l’ús de tècniques de refinament adaptatiu de la malla, alhora que es manté la localitat i compacitat dels esquemes DG. En segon lloc, es proposa una tècnica clàssica i, aparentment simple: la introducció de la viscositat artificial. Primerament es realitza un estudi detallat per al cas unidimensional. S’obté una viscositat d’alta precisió que escala segons el valor hk amb 1 ≤ k ≤ p i essent h la mida de l’element. En conseqüència, s’obté un xoc amb amplitud del mateix ordre. Seguidament, l'estudi de la viscositat unidimensional obtenida s'extén al cas multidimensional per a malles triangulars. L'extensió es basa en la projecció de la viscositat unidimensional en unes determinades direccions espacials dins l’element. Es demostra de manera consistent que la viscositat introduïda és, com a molt, del mateix ordre que la resolució donada per la discretització espacial, és a dir, h/p. El mètode és especialment eficient per aproximacions de Galerkin discontinu d’alt ordre, per exemple p≥ 3. Les dues metodologies es validen mitjançant una àmplia selecció d’exemples numèrics. En alguns exemples, els mètodes proposats permeten una reducció en el nombre de graus de llibertat necessaris per capturar xocs acuradament de fins i tot un ordre de magnitud, en comparació amb mètodes estàndar de refinament adaptatiu amb aproximacions de baix ordre.
This thesis proposes shock-capturing methods for high-order Discontinuous Galerkin (DG) formulations providing highly accurate solutions for compressible flows. In the last decades, research in DG methods has been very active. The success of DG in hyperbolic problems has driven many studies for nonlinear conservation laws and convection-dominated problems. Among all the advantages of DG, their inherent stability and local conservation properties are relevant. Moreover, DG methods are naturally suited for high-order approximations. Actually, in recent years it has been shown that convection-dominated problems are no longer restricted to low-order elements. In fact, highly accurate numerical models for High-Fidelity predictions in CFD are necessary. Under this rationale, two shock-capturing techniques are presented and discussed. First, a novel and simple technique based on on the introduction of a new basis of shape functions is presented. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization thanks to the numerical fluxes, thus exploiting DG inherent properties. Large high-order elements can therefore be used and shocks are captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Second, a classical and, apparently simple, technique is advocated: the introduction of artificial viscosity. First, a one-dimensional study is perfomed. Viscosity of the order O(hk) with 1≤ k≤ p is obtained, hence inducing a shock width of the same order. Second, the study extends the accurate one-dimensional viscosity to triangular multidimensional meshes. The extension is based on the projection of the one-dimensional viscosity into some characteristic spatial directions within the elements. It is consistently shown that the introduced viscosity scales, at most, withthe DG resolutions length scales, h/p. The method is especially reliable for highorder DG approximations, say p≥3. A wide range of different numerical tests validate both methodologies. In some examples the proposed methods allow to reduce by an order of magnitude the number of degrees of freedom necessary to accurately capture the shocks, compared to standard low order h-adaptive approaches.
APA, Harvard, Vancouver, ISO, and other styles
9

Dong, Zhaonan. "Discontinuous Galerkin methods on polytopic meshes." Thesis, University of Leicester, 2017. http://hdl.handle.net/2381/39140.

Full text
Abstract:
This thesis is concerned with the analysis and implementation of the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) on computational meshes consisting of general polygonal/polyhedral (polytopic) elements. Two model problems are considered: general advection-diffusion-reaction boundary value problems and time dependent parabolic problems. New hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration as well as an arbitrary number of faces and hanging nodes per element. The proposed method employs elemental polynomial bases of total degree p (Pp- bases) defined in the physical coordinate system, without requiring mapping from a given reference or canonical frame. A series of numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a Pp-basis on both polytopic and tensor-product elements with a (standard) DGFEM and FEM employing a (mapped) Qp-basis. Moreover, a careful theoretical analysis of optimal convergence rate in p for Pp-basis is derived for several commonly used projectors, which leads to sharp bounds of exponential convergence with respect to degrees of freedom (dof) for the Pp-basis.
APA, Harvard, Vancouver, ISO, and other styles
10

Elfverson, Daniel. "Discontinuous Galerkin Multiscale Methods for Elliptic Problems." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138960.

Full text
Abstract:
In this paper a continuous Galerkin multiscale method (CGMM) and a discontinuous Galerkin multiscale method (DGMM) are proposed, both based on the variational multiscale method for solving partial differential equations numerically. The solution is decoupled into a coarse and a fine scale contribution, where the fine-scale contribution is computed on patches with localized right hand side. Numerical experiments are presented where exponential decay of the error is observed when increasing the size of the patches for both CGMM and DGMM. DGMM gives much better accuracy when the same size of the patches are used.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Discontinous Galerkin method"

1

Dolejší, Vít, and Miloslav Feistauer. Discontinuous Galerkin Method. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Cockburn, Bernardo, George E. Karniadakis, and Chi-Wang Shu, eds. Discontinuous Galerkin Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-59721-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Hesthaven, Jan S., and Tim Warburton. Nodal Discontinuous Galerkin Methods. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-72067-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Bottasso, Carlo L. Discontinuous dual-primal mixed finite elements for elliptic problems. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2000.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Pietro, Daniele Antonio Di. Mathematical aspects of discontinuous galerkin methods. Berlin: Springer, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

1967-, Ern Alexandre, ed. Mathematical aspects of discontinuous galerkin methods. Berlin: Springer, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Di Pietro, Daniele Antonio, and Alexandre Ern. Mathematical Aspects of Discontinuous Galerkin Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-22980-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Hu, Chang-Qing. A discontinuous Galerkin finite element method for Hamilton-Jacobi equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Cockburn, B. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Hampton, VA: ICASE, NASA Langley Research Center, 2000.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Yan, Jue. Local discontinuous Galerkin methods for partial differential equations with higher order derivates. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Discontinous Galerkin method"

1

Dolejší, Vít, and Miloslav Feistauer. "Space-Time Discontinuous Galerkin Method." In Discontinuous Galerkin Method, 223–335. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Dolejší, Vít, and Miloslav Feistauer. "Space-Time Discretization by Multistep Methods." In Discontinuous Galerkin Method, 171–222. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Dolejší, Vít, and Miloslav Feistauer. "Introduction." In Discontinuous Galerkin Method, 1–23. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Dolejší, Vít, and Miloslav Feistauer. "Fluid-Structure Interaction." In Discontinuous Galerkin Method, 521–51. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Dolejší, Vít, and Miloslav Feistauer. "DGM for Elliptic Problems." In Discontinuous Galerkin Method, 27–84. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Dolejší, Vít, and Miloslav Feistauer. "Methods Based on a Mixed Formulation." In Discontinuous Galerkin Method, 85–115. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Dolejší, Vít, and Miloslav Feistauer. "DGM for Convection-Diffusion Problems." In Discontinuous Galerkin Method, 117–69. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Dolejší, Vít, and Miloslav Feistauer. "Generalization of the DGM." In Discontinuous Galerkin Method, 337–97. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Dolejší, Vít, and Miloslav Feistauer. "Inviscid Compressible Flow." In Discontinuous Galerkin Method, 401–75. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Dolejší, Vít, and Miloslav Feistauer. "Viscous Compressible Flow." In Discontinuous Galerkin Method, 477–519. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19267-3_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Discontinous Galerkin method"

1

Lörcher, Frieder, Gregor Gassner, and Claus-Dieter Munz. "Space-Time Discontinous Galerkin Method for Unsteady Compressible Navier-Stokes Equations." In 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference). Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-3477.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Bagherli, Hamid, and Ian Jeffrey. "H-matrix compression of discontinous Galerkin method exact radiating boundary conditions." In 2016 17th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM). IEEE, 2016. http://dx.doi.org/10.1109/antem.2016.7550229.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Durochat, C., S. Lanteri, L. Moya, J. Viquerat, S. Descombes, and C. Scheid. "Some recent developments of the discontinous Galerkin method for time-domain electromagnetics." In THE FIFTH INTERNATIONAL WORKSHOP ON THEORETICAL AND COMPUTATIONAL NANO-PHOTONICS: TaCoNa-Photonics 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4750079.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Wang, Junfeng, Chunlei Liang, and Charles A. Garris. "Two-Dimensional Discontinous Galerkin Simulations of Crypto-Steady Supersonic Pressure Exchange." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65818.

Full text
Abstract:
This paper reports the development of a third-order discontinuous Galerkin (DG) method for supersonic inviscid flow on a moving grid, as well as simulations of a simple model of crypto-steady supersonic pressure exchange (CSSPE) by solving 2D inviscid Euler equations. A total variation bounded (TVB) limiter is implemented for shock capturing. The third-order DG method is firstly validated using a case of supersonic vortex flow. Subsequently, the method is successfully employed to predict the crypto-steady supersonic flat-plate flow under various pressure ratios. In particular, at high pressure ratios between primary gas and secondary gas, a detached shock away from the trailing edge of the flat plate is accurately predicted. This study is our first step in approaching to developing a 3D numerical tool and modeling a novel pressure-exchange ejector.
APA, Harvard, Vancouver, ISO, and other styles
5

Meilin Liu and H. Bagci. "A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations." In 2011 IEEE Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting. IEEE, 2011. http://dx.doi.org/10.1109/aps.2011.5997233.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Busch, Kurt. "Discontinuous Galerkin Methods in Nanophotonics." In Integrated Photonics Research, Silicon and Nanophotonics. Washington, D.C.: OSA, 2012. http://dx.doi.org/10.1364/iprsn.2012.im3b.1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Cockburn, Bernardo. "The Hybridizable Discontinuous Galerkin Methods." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0166.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Peyret, Christophe, and Philippe Delorme. "Discontinuous Galerkin Method for Computational Aeroacoustics." In 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference). Reston, Virigina: American Institute of Aeronautics and Astronautics, 2006. http://dx.doi.org/10.2514/6.2006-2568.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Kim, Cheolwan, H. Chang, and Jang Yeon Lee. "Compact Higher-order Discontinuous Galerkin Method." In 11th AIAA/CEAS Aeroacoustics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-2824.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Collis, S. Scott, and Kaveh Ghayour. "Discontinuous Galerkin Methods for Compressible DNS." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45632.

Full text
Abstract:
A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to a range of test problems including steady and unsteady flow over a circular cylinder, inviscid flow over an inclined ellipse, and fully developed turbulent flow in a planar channel. In all cases, local hp-refinement is utilized to obtain high quality solutions with fewer degrees of freedom than traditional numerical methods. The formulation and validation cases presented here lay the foundation for future applications of DG for simulation of compressible turbulent flows in complex geometries.
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Discontinous Galerkin method"

1

Lin, Guang, and George E. Karniadakis. A Discontinuous Galerkin Method for Two-Temperature Plasmas. Fort Belvoir, VA: Defense Technical Information Center, March 2005. http://dx.doi.org/10.21236/ada458981.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Garikipati, Krishna, and Jakob T. Ostien. Discontinuous Galerkin finite element methods for gradient plasticity. Office of Scientific and Technical Information (OSTI), October 2010. http://dx.doi.org/10.2172/1008112.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Watkins, Jerry. Current Status of Discontinuous Galerkin (DG) methods in SPARC. Office of Scientific and Technical Information (OSTI), September 2019. http://dx.doi.org/10.2172/1564038.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Shu, Chi-Wang. Final Technical Report: High Order Discontinuous Galerkin Method and Applications. Office of Scientific and Technical Information (OSTI), March 2019. http://dx.doi.org/10.2172/1499046.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Xia, Yinhua, Yan Xu, and Chi-Wang Shu. Local Discontinuous Galerkin Methods for the Cahn-Hilliard Type Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2007. http://dx.doi.org/10.21236/ada464873.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Romkes, A., S. Prudhomme, and J. T. Oden. A Posteriori Error Estimation for a New Stabilized Discontinuous Galerkin Method. Fort Belvoir, VA: Defense Technical Information Center, August 2002. http://dx.doi.org/10.21236/ada438102.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Nourgaliev, R., H. Luo, S. Schofield, T. Dunn, A. Anderson, B. Weston, and J. Delplanque. Fully-Implicit Orthogonal Reconstructed Discontinuous Petrov-Galerkin Method for Multiphysics Problems. Office of Scientific and Technical Information (OSTI), February 2015. http://dx.doi.org/10.2172/1178386.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Laeuter, Matthias, Francis X. Giraldo, Doerthe Handorf, and Klaus Dethloff. A Discontinuous Galerkin Method for the Shallow Water Equations in Spherical Triangular Coordinates. Fort Belvoir, VA: Defense Technical Information Center, November 2007. http://dx.doi.org/10.21236/ada486030.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Bui-Thanh, Tan, and Omar Ghattas. Analysis of an Hp-Non-conforming Discontinuous Galerkin Spectral Element Method for Wave. Fort Belvoir, VA: Defense Technical Information Center, April 2011. http://dx.doi.org/10.21236/ada555327.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Wang, Wei, Xiantao Li, and Chi-Wang Shu. The Discontinuous Galerkin Method for the Multiscale Modeling of Dynamics of Crystalline Solids. Fort Belvoir, VA: Defense Technical Information Center, August 2007. http://dx.doi.org/10.21236/ada472151.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Discontinous Galerkin method' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography