Relevant bibliographies by topics / High-Order finite element methods

Contents

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

Academic literature on the topic 'High-Order finite element methods'

Author: Grafiati
Published: 8 June 2024
Last updated: 31 July 2025

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Journal articles on the topic "High-Order finite element methods"

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Abreu, Eduardo, Ciro Díaz, Juan Galvis, and Marcus Sarkis. "On high-order conservative finite element methods." Computers & Mathematics with Applications 75, no. 6 (2018): 1852–67. http://dx.doi.org/10.1016/j.camwa.2017.10.020.

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Harari, Isaac, and Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems." Journal of Computational Acoustics 05, no. 01 (1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.

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The goal of this work is to design and analyze quadratic finite elements for problems of time-harmonic acoustics, and to compare the computational efficiency of quadratic elements to that of lower-order elements. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solutions to exterior problems. Galerkin/least-squares technology is utilized to develop robust methods in which stability properties are enhanced while maintaining higher-order accuracy. The design of Galerkin/least-squares methods depends on the order
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Bagheri, Babak, L. Ridgway Scott, and Shangyou Zhang. "Implementing and using high-order finite element methods." Finite Elements in Analysis and Design 16, no. 3-4 (1994): 175–89. http://dx.doi.org/10.1016/0168-874x(94)90063-9.

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Lin, Qun, and Junming Zhou. "Superconvergence in high-order Galerkin finite element methods." Computer Methods in Applied Mechanics and Engineering 196, no. 37-40 (2007): 3779–84. http://dx.doi.org/10.1016/j.cma.2006.10.027.

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Larson, Mats G., and Sara Zahedi. "Stabilization of high order cut finite element methods on surfaces." IMA Journal of Numerical Analysis 40, no. 3 (2019): 1702–45. http://dx.doi.org/10.1093/imanum/drz021.

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Abstract We develop and analyse a stabilization term for cut finite element approximations of an elliptic second-order partial differential equation on a surface embedded in ${\mathbb{R}}^d$. The new stabilization term combines properly scaled normal derivatives at the surface together with control of the jump in the normal derivatives across faces, and provides control of the variation of the finite element solution on the active three-dimensional elements that intersect the surface. We show that the condition number of the stiffness matrix is $O(h^{-2})$, where $h$ is the mesh parameter. The
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Winther, Kaibo Hu &. Ragnar. "Well-Conditioned Frames for High Order Finite Element Methods." Journal of Computational Mathematics 39, no. 3 (2021): 333–57. http://dx.doi.org/10.4208/jcm.2001-m2018-0078.

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Dobrev, Veselin A., Tzanio V. Kolev, and Robert N. Rieben. "High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics." SIAM Journal on Scientific Computing 34, no. 5 (2012): B606—B641. http://dx.doi.org/10.1137/120864672.

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Yurun, Fan, and M. J. Crochet. "High-order finite element methods for steady viscoelastic flows." Journal of Non-Newtonian Fluid Mechanics 57, no. 2-3 (1995): 283–311. http://dx.doi.org/10.1016/0377-0257(94)01338-i.

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Opschoor, Joost A. A., Philipp C. Petersen, and Christoph Schwab. "Deep ReLU networks and high-order finite element methods." Analysis and Applications 18, no. 05 (2020): 715–70. http://dx.doi.org/10.1142/s0219530519410136.

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Approximation rate bounds for emulations of real-valued functions on intervals by deep neural networks (DNNs) are established. The approximation results are given for DNNs based on ReLU activation functions. The approximation error is measured with respect to Sobolev norms. It is shown that ReLU DNNs allow for essentially the same approximation rates as nonlinear, variable-order, free-knot (or so-called “[Formula: see text]-adaptive”) spline approximations and spectral approximations, for a wide range of Sobolev and Besov spaces. In particular, exponential convergence rates in terms of the DNN
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Jund, Sébastien, and Stéphanie Salmon. "Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping." International Journal of Applied Mathematics and Computer Science 17, no. 3 (2007): 375–93. http://dx.doi.org/10.2478/v10006-007-0031-2.

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Arbitrary High-Order Finite Element Schemes and High-Order Mass LumpingComputers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of orderkand show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also constr
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Dissertations / Theses on the topic "High-Order finite element methods"

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Marais, Neilen. "Efficient high-order time domain finite element methods in electromagnetics." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/1499.

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Thesis (DEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009.<br>The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can beused to solve a large class of Electromagnetics problems with high accuracy and good computational efficiency. For solving wide-band problems time domain solutions are often preferred; while time domain FEM methods are feasible, the Finite Difference Time Domain (FDTD) method is more commonly applied. The FDTD is popular both for its efficiency and its simplicity. The efficiency of the FDTD stems from the fact tha
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Franke, David [Verfasser]. "Investigation of mechanical contact problems with high-order Finite Element Methods / David Franke." Aachen : Shaker, 2012. http://d-nb.info/1067734902/34.

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Al-Shanfari, Fatima. "High-order in time discontinuous Galerkin finite element methods for linear wave equations." Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/15332.

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In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract approximation analysis is a generalisation of the approach introduced by Claes Johnson (in Comput. Methods Appl. Mech. Engrg., 107:117-129, 1993), writing the second order problem as a system of fi rst order problems. We consider abstract spatial (time independent) operators, highorder in time basis functions when discretising in time; we also prove approximation results in case of linear constraints, e.g. non-homogeneous boun
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Marrett, Sean 1960. "A high-order finite element method for Tokamak plasma equilibria /." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=56809.

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A numerical method for the solution of the axisymmetric, free-boundary, Tokamak equilibrium problem is described. The method uses high-order polynomials defined over a mesh of triangular finite elements to solve the magnetohydrodynamic equilibrium (Grad-Shafranov) equation. Arbitrary coil and plasma current configurations can be specified. The formulation incorporates a nonlinear procedure for computing the coil currents required to place the plasma in a desired position. The solution to the nonlinear Grad-Shafranov equation is computed using a modified Newton's method. The inner-most system o
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Moura, Rodrigo Costa. "A high-order unstructured discontinuous galerkin finite element method for aerodynamics." Instituto Tecnológico de Aeronáutica, 2012. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2158.

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The present thesis discuss in a didactic and detailed way the high-order scheme known as the Discontinuous Galerkin (DG) method, with special focus on applications in aerodynamics. The theoretical formulation of the method is presented in one and two dimensions with great depth, being properly discussed issues of convergence, basis functions, interelement communication, boundary conditions, shock treatment, as well as inviscid and viscous numerical fluxes. As part of this effort, a parallel computer code was developed to simulate the Euler equations of gas dynamics in two dimensions with gener
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Guo, Ruchi. "Design, Analysis, and Application of Immersed Finite Element Methods." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90374.

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This dissertation consists of three studies of immersed finite element (IFE) methods for inter- face problems related to partial differential equations (PDEs) with discontinuous coefficients. These three topics together form a continuation of the research in IFE method including the extension to elasticity systems, new breakthroughs to higher degree IFE methods, and its application to inverse problems. First, we extend the current construction and analysis approach of IFE methods in the literature for scalar elliptic equations to elasticity systems in the vector format. In particular, we cons
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Chuang, Shih-Chang. "Parallel methods for high-performance finite element methods based on sparsity." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/18177.

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Zhou, Dong. "High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/295839.

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Mathematics<br>Ph.D.<br>Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity
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Couchman, Benjamin Luke Streatfield. "On the convergence of higher-order finite element methods to weak solutions." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115685.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 77-79).<br>The ability to handle discontinuities appropriately is essential when solving nonlinear hyperbolic partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a di
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Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.

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Aquesta tesi proposa una millora del clàssic mètode dels elements finits (finite element method, FEM) per a un tractament eficient de dominis amb contorns corbs: el denominat NURBS-enhanced finite element method (NEFEM). Aquesta millora permet descriure de manera exacta la geometría mitjançant la seva representació del contorn CAD amb non-uniform rational B-splines (NURBS), mentre que la solució s'aproxima amb la interpolació polinòmica estàndard. Per tant, en la major part del domini, la interpolació i la integració numèrica són estàndard, retenint les propietats de convergència clàssiques de
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Books on the topic "High-Order finite element methods"

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Karel, Segeth, and Dolez̆el Ivo, eds. Higher-order finite element methods. Chapman & Hall/CRC, 2004.

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Vandandoo, Ulziibayar, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, and Galmandakh Chuluunbaatar. High-Order Finite Difference and Finite Element Methods for Solving Some Partial Differential Equations. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-44784-6.

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University of Wales. Institute for Numerical Methods in Engineering. and Langley Research Center. Aerothermal Loads Branch., eds. Finite element methods of analysis for high speed viscous flows. Aerothermal Loads Branch, Loads and Aeroelasticity Division, NASA Langley Research Center, 1987.

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Zhang, Yong-Tao. High order WENO schemes for Hamilton-Jacobi equations on triangular meshes. ICASE, NASA Langley Research Center, 2001.

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George C. Marshall Space Flight Center., ed. Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows. NASA-Marshall Space Flight Center, 1988.

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George C. Marshall Space Flight Center., ed. Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows. NASA-Marshall Space Flight Center, 1988.

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

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Hsing-jen, Chang, and Langley Research Center, eds. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. National Aeronautics and Space Administration, Langley Research Center, 1993.

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Xingren, Zhang, and Langley Research Center, eds. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. National Aeronautics and Space Administration, Langley Research Center, 1993.

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Hsing-jen, Chang, and Langley Research Center, eds. H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows. National Aeronautics and Space Administration, Langley Research Center, 1993.

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Book chapters on the topic "High-Order finite element methods"

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Lyu, Yongtao. "High Order Lagrange Element." In Finite Element Method. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3363-9_8.

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Khursheed, Anjam. "High-Order Elements." In The Finite Element Method in Charged Particle Optics. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5201-7_5.

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Duczek, S., C. Willberg, and U. Gabbert. "Higher Order Finite Element Methods." In Lamb-Wave Based Structural Health Monitoring in Polymer Composites. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49715-0_6.

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Lin, Qun. "High Performance Finite Element Methods." In Recent Progress in Computational and Applied PDES. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0113-8_20.

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Schöberl, Joachim, and Christoph Lehrenfeld. "Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes." In Advanced Finite Element Methods and Applications. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30316-6_2.

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St.-Cyr, Amik, and Stephen J. Thomas. "High-Order Finite Element Methods for Parallel Atmospheric Modeling." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11428831_32.

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Sabonnadière, Jean-Claude, and Jean-Louis Coulomb. "General theory of second order isoparametric elements." In Finite Element Methods in CAD. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4684-8739-8_5.

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Sabonnadière, Jean-Claude, and Jean-Louis Coulomb. "General theory of second order isoparametric elements." In Finite Element Methods in CAD. Springer US, 1987. http://dx.doi.org/10.1007/978-1-4615-9879-4_5.

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Cuvelier, C., A. Segal, and A. A. van Steenhoven. "Second Order Elliptic PDEs." In Finite Element Methods and Navier-Stokes Equations. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_11.

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Kyriakoudi, Konstantina C., and Michail A. Xenos. "Finite Element Methods with Higher Order Polynomials." In Exploring Mathematical Analysis, Approximation Theory, and Optimization. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-46487-4_10.

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Conference papers on the topic "High-Order finite element methods"

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Daniels, Bram, Mitrofan Curti, Timo Overboom, and Elena Lomonova. "Comparison of the Finite Element Method and High-Order Isogeometric Analysis for Modeling Magnetic Vector Hysteresis." In 2024 IEEE 21st Biennial Conference on Electromagnetic Field Computation- Extended Papers (CEFC-Extended). IEEE, 2024. https://doi.org/10.1109/cefc65091.2024.10849020.

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Nourgaliev, R., A. Corrigan, A. Kercher, S. Wopschall, and P. Greene. "Implicit Shock Fitting for Multimaterial Shock Dynamics Using a High-Order Space-Time Discontinuous Finite-Element Method." In Mathematics and Computation 2021. American Nuclear Society, 2021. https://doi.org/10.13182/xyz-33817.

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D'Aquila, Luke, Brian Helenbrook, and Alireza Mazaheri. "High-Order Shock Fitting with Finite Element Methods." In AIAA AVIATION 2020 FORUM. American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-3047.

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Kollmannsberger, Stefan, Alexander Du¨ster, and Ernst Rank. "Force Transfer for High Order Finite Element Methods Using Intersected Meshes." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26539.

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High order Finite Element Methods have been shown to be an efficient approach for computing the behavior of fluids and structures alike. However the coupling of such methods in a framework for a partitioned fluid-structure interaction is still in its early stages. A difficulty hereby is a conservative transfer of the loads from the fluid to the solid and an appropriate transfer of the structural displacements back to the boundary of the fluid. This contribution describes the coupling of a high order finite element structural code to the commercial finite volume fluid solver CFX and focuses on
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Woopen, Michael, Aravind Balan, and Georg May. "A Unifying Computational Framework for Adaptive High-Order Finite Element Methods." In 22nd AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2015. http://dx.doi.org/10.2514/6.2015-2601.

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Shumlak, U., R. Lilly, S. Miller, N. Reddell, and E. Sousa. "High-order finite element method for plasma modeling." In 2013 IEEE 40th International Conference on Plasma Sciences (ICOPS). IEEE, 2013. http://dx.doi.org/10.1109/plasma.2013.6634927.

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Shumlak, U., R. Lilly, S. Miller, N. Reddell, and E. Sousa. "High-order finite element method for plasma modeling." In 2013 IEEE Pulsed Power and Plasma Science Conference (PPPS 2013). IEEE, 2013. http://dx.doi.org/10.1109/ppc.2013.6627593.

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Sheshadri, Abhishek, and Antony Jameson. "Shock detection and capturing methods for high order Discontinuous-Galerkin Finite Element Methods." In 32nd AIAA Applied Aerodynamics Conference. American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-2688.

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Shumlak, U., J. B. Coughlin, D. W. Crews, et al. "High-Order Finite Element Method for High-Fidelity Plasma Modeling." In 2020 IEEE International Conference on Plasma Science (ICOPS). IEEE, 2020. http://dx.doi.org/10.1109/icops37625.2020.9717941.

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Wang, Li, W. Kyle Anderson, and Lafayette K. Taylor. "Multiscale Large Eddy Simulation of Turbulence Using High-Order Finite Element Methods." In 7th AIAA Theoretical Fluid Mechanics Conference. American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-3211.

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Reports on the topic "High-Order finite element methods"

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Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Defense Technical Information Center, 2008. http://dx.doi.org/10.21236/ada500484.

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Kirby, Robert M., and Robert Haimes. Visualization of High-Order Finite Element Methods. Defense Technical Information Center, 2013. http://dx.doi.org/10.21236/ada578239.

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Gao, Kai. Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation. Office of Scientific and Technical Information (OSTI), 2018. http://dx.doi.org/10.2172/1481964.

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Adjerid, Slimane, Mohammed Aiffa, and Joseph E. Flaherty. High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada290410.

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White, D., M. Stowell, J. Koning, et al. Higher-Order Mixed Finite Element Methods for Time Domain Electromagnetics. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/15014733.

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Dobrev, V. A., F. C. Grogan, T. V. Kolev, R. Rieben, and V. Z. Tomov. Level set methods for detonation shock dynamics using high-order finite elements. Office of Scientific and Technical Information (OSTI), 2017. http://dx.doi.org/10.2172/1361591.

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Rieben, Robert N. A Novel High Order Time Domain Vector Finite Element Method for the Simulation of Electromagnetic Devices. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/15014486.

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Graville. L51764 Hydrogen Cracking in the Heat-Affected Zone of High-Strength Steels-Year 2. Pipeline Research Council International, Inc. (PRCI), 1997. http://dx.doi.org/10.55274/r0010170.

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During year 1 of this project a test to evaluate the sensitivity of the heat affected zone (HAZ) to hydrogen cracking was developed. This was in response to a need for a test which provided unambiguous results in contrast to existing test methods which often led to difficulties in interpretation. For example, WIC tests usually cracked in the weld metal rather than the HAZ and therefore did not produce a clear indication of the sensistivity of the HAZ. The new test involves a machined notch which can be placed in the HAZ thus forcing crack initiation to occur in the desired region. A further ad
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Pasupuleti, Murali Krishna. Mathematical Modeling for Machine Learning: Theory, Simulation, and Scientific Computing. National Education Services, 2025. https://doi.org/10.62311/nesx/rriv125.

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Abstract Mathematical modeling serves as a fundamental framework for advancing machine learning (ML) and artificial intelligence (AI) by integrating theoretical, computational, and simulation-based approaches. This research explores how numerical optimization, differential equations, variational inference, and scientific computing contribute to the development of scalable, interpretable, and efficient AI systems. Key topics include convex and non-convex optimization, physics-informed machine learning (PIML), partial differential equation (PDE)-constrained AI, and Bayesian modeling for uncertai
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Chauhan. L52134 Development of Methods For Assessing Corrosion Metal Loss Defects In Casing Strings. Pipeline Research Council International, Inc. (PRCI), 2003. http://dx.doi.org/10.55274/r0010892.

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An industry survey, dominated by PRCI member companies, was undertaken to gather key information regarding the design, operation and inspection of well bore casing strings. The aim of the survey was to gather information regarding the design standards, fields, gas composition, completion configuration, operational details, inspection methods and type of damage found. Survey results representing 67 storage facilities with a total of 4724 wells were received. This represents approximately 16% of US gas storage facilities. Facilities with initial completion dates between 1920 and 1990 were repres
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