Relevant bibliographies by topics / Lax-Friedrichs

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Academic literature on the topic 'Lax-Friedrichs'

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

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Journal articles on the topic "Lax-Friedrichs"

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Shampine, L. F. "Two-step Lax–Friedrichs method." Applied Mathematics Letters 18, no. 10 (October 2005): 1134–36. http://dx.doi.org/10.1016/j.aml.2004.11.007.

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Yu, Simin. "A survey of numerical schemes for transportation equation." E3S Web of Conferences 308 (2021): 01020. http://dx.doi.org/10.1051/e3sconf/202130801020.

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The convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly characterizes natural phenomenon in which physical particles, energy are transferred in a system. The well-known linear transport equation is also one kind of convection-diffusion equation. The transport equation can describe the transport of a scalar field such as material feature, chemical reaction or temperature in an incompressible flow. In this paper, we discuss the famous numerical scheme, Lax-Friedrichs method, for the linear transport equation. The important ingredient of the design of the Lax-Friedrichs Method, namely the choice of the numerical fluxes will be discussed in detail. We give a detailed proof of the L1 stability of the Lax-Friedrichs scheme for the linear transport equation. We also address issues related to the implementation of this numerical scheme.
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Breuß, Michael. "The correct use of the Lax–Friedrichs method." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 3 (May 2004): 519–40. http://dx.doi.org/10.1051/m2an:2004027.

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Bodnár, Tomáš, Philippe Fraunié, and Karel Kozel. "MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM." Acta Polytechnica 61, SI (February 10, 2021): 49–58. http://dx.doi.org/10.14311/ap.2021.61.0049.

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This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods.
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Marcati, Pierangelo, and Roberto Natalini. "Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 115–31. http://dx.doi.org/10.1017/s030821050003078x.

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We investigate the Cauchy problem for a hydrodynamic model for semiconductors. An existence theorem of global weak solutions with large initial data is obtained by using the fractional step Lax—Friedrichs scheme and Godounov scheme.
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Dallakyan, Gurgen. "Numerical Simulations for Chemotaxis Models." Biomath Communications 6, no. 1 (May 11, 2019): 16. http://dx.doi.org/10.11145/bmc.2019.04.277.

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In the paper, we study the usage of numerical methods in solution of mathematical models of biological problems. More specifically, Keller-Segel type chemotaxis models are discussed, their numerical solutions by sweep and Lax-Friedrichs methods are obtained and interpreted biologically.
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Soga, Kohei. "Stochastic and variational approach to the Lax-Friedrichs scheme." Mathematics of Computation 84, no. 292 (July 22, 2014): 629–51. http://dx.doi.org/10.1090/s0025-5718-2014-02863-9.

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Kao, Chiu Yen, Stanley Osher, and Jianliang Qian. "Lax–Friedrichs sweeping scheme for static Hamilton–Jacobi equations." Journal of Computational Physics 196, no. 1 (May 2004): 367–91. http://dx.doi.org/10.1016/j.jcp.2003.11.007.

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JOVANOVIC, V. "Error Estimates For The Lax — Friedrichs Scheme For Balance Laws." Computational Methods in Applied Mathematics 8, no. 2 (2008): 130–42. http://dx.doi.org/10.2478/cmam-2008-0009.

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AbstractWe first derive the general error estimate for one – dimensional balance laws and afterwards we apply it to the elastodynamics system with source and to the isentropic Euler system with damping.
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Baiti, Paolo, Alberto Bressan, and Helge Kristian Jenssen. "Instability of travelling wave profiles for the Lax-Friedrichs scheme." Discrete & Continuous Dynamical Systems - A 13, no. 4 (2005): 877–99. http://dx.doi.org/10.3934/dcds.2005.13.877.

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Dissertations / Theses on the topic "Lax-Friedrichs"

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Bedjaoui, Nabil, Joaquim Correia, Sackmone Sirisack, and Bouasy Doungsavanh. "Traffic Modelling and Some Inequalities in Banach Spaces." Master's thesis, Edited by Thepsavanh Kitignavong, Faculty of Natural Sciences, National University of Laos, 2017. http://hdl.handle.net/10174/26575.

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Modelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what happens as time evolves if we fix at initial time (t = 0) some special distribution of cars (initial datum u_0). Because we do approximations, we need the notion of convergence and its corresponding topology. The numerical approximation of scalar conservation laws is carried out by using conservative methods such as the Lax-Friedrichs and the Lax-Wendroff schemes. The Lax-Friedrichs scheme gives regular numerical solutions even when the exact solution is discontinuous (shock waves). We say the scheme is diffusive meaning that the scheme is solving in fact an evolution equation of the form u_t+f(u)_x = epsilon u_xx, where epsilon is a small parameter depending on ∆x and ∆t. The Lax-Wendroff scheme is more precise than the Lax-Friedrichs scheme, and give the right position of the discontinuities for the shock waves. But it develop oscillations. We say the scheme is dispersive what means the scheme is solving approximatively an evolution equation of the form u_t + f(u)_x = delta u_xxx, where delta is a small parameter depending on ∆x and ∆t. An elaboration and an implementation of Lax-Friedrichs schemes and of Lax-Wendroff schemes even extended to second order provided numerical solutions to the problem of traffic flows on the road. Since along the roads the schemes present the same features as for conservation laws, the new and original aspect is given by the treatment of the solution at junctions. Our tests show the effectiveness of the approximations, revealing that Lax-Wendroff schemes is more accurate than Lax-Friedrichs schemes.
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Panko, Martin. "Tlumení tlakových pulsací v pružných potrubích." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2008. http://www.nusl.cz/ntk/nusl-228178.

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This diploma thesis deals with numerical simulation of pressure pulsations in elastic pipes. Continuity relation of fluid in elastic pipes, when calculating some damping in pipe material, is derived into practice. Rheological model of such a pipe corresponds to Voigt (Kelvin) model. For analysing dynamic effects in time periods are used numerical methods that deal with flow of compressible fluid: FTCS, Lax-Friedrichs and Lax-Wendroff method. The numerical results are confronted with the experiment. During the experiment simulation the method considers speed of sound in liquid like a function of pressure. This diploma thesis lays partial principles for finding elastic constants for describing dynamic characteristics of elastic pipes by measuring the pressure pulsations.
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Akturk, Ali. "Two-dimensional Finite Volume Weighted Essentially Non-oscillatory Euler Schemes With Different Flux Algorithms." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606387/index.pdf.

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The purpose of this thesis is to implement Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) scheme to solution of one and two-dimensional discretised Euler equations with different flux algorithms. The effects of the different fluxes on the solution have been tested and discussed. Beside, the effect of the grid on these fluxes has been investigated. Weighted Essentially Non-Oscillatory (WENO) schemes are high order accurate schemes designed for problems with piecewise smooth solutions that involve discontinuities. WENO schemes have been successfully used in applications, especially for problems containing both shocks and complicated smooth solution structures. Fluxes are used as building blocks in FV-WENO scheme. The efficiency of the scheme is dependent on the fluxes used in scheme The applications tested in this thesis are the 1-D Shock Tube Problem, Double Mach Reflection, Supersonic Channel Flow, and supersonic Staggered Wedge Cascade. The numerical solutions for 1-D Shock Tube Problem and the supersonic channel flow are compared with the analytical solutions. The results for the Double Mach Reflection and the supersonic staggered cascade are compared with results from literature.
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Chen, Weitao. "Fast Sweeping Methods for Steady State Hyperbolic Conservation Problems and Numerical Applications for Shape Optimization and Computational Cell Biology." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366279632.

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St-Cyr, Amik. "Construction de méthodes de volumes finis tridimensionnelles sans solveur de Riemann pour les systèmes hyperboliques non-linéaires." Thèse, 2002. http://hdl.handle.net/1866/6743.

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Books on the topic "Lax-Friedrichs"

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Edmunds, D. E., and W. D. Evans. Sesquilinear Forms in Hilbert Spaces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0004.

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The centre-pieces of this chapter are the Lax–Milgram Theorem and the existence of weak or variational solutions to problems involving sesquilinear forms. An important application is to Kato’s First Representation Theorem, which associates a unique m-sectorial operator with a closed, densely defined sesquilinear form, thus extending the Friedrichs extension for a lower bounded symmetric operator. Stampacchia’s generalization of the Lax–Milgram Theorem to variational inequalities is also discussed.
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Book chapters on the topic "Lax-Friedrichs"

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Tong, Wei, and Yun Wu. "Generalized Lax-Friedrichs Scheme for Convective-Diffusion Equation." In Communications in Computer and Information Science, 321–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34038-3_44.

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Jiang, Haixin, and Wei Tong. "New Lax-Friedrichs Scheme for Convective-Diffusion Equation." In Information Computing and Applications, 269–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34062-8_35.

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Wu, Yun, Hai-xin Jiang, and Wei Tong. "Generalized Lax-Friedrichs Schemes for Linear Advection Equation with Damping." In Information Computing and Applications, 305–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25255-6_39.

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Godillon-Lafitte, Pauline. "Green’s Function Pointwise Estimates for the Modified Lax-Friedrichs Scheme." In Hyperbolic Problems: Theory, Numerics, Applications, 539–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55711-8_50.

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Haasdonk, Bernard. "Convergence of a Staggered Lax-Friedrichs Scheme on Unstructured 2D-grids." In Hyperbolic Problems: Theory, Numerics, Applications, 475–83. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8372-6_1.

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Arminjon, P., A. St-Cyr, and A. Madrane. "Non-oscillatory Lax-Friedrichs Type Central Finite Volume Methods for 3-D Flows on Unstructured Tetrahedral Grids." In Hyperbolic Problems: Theory, Numerics, Applications, 59–68. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8370-2_7.

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Morawetz, Cathleen S. "Boundary value problems for first order operators, (With Peter D. Lax), Comm. Pure Appl. Math., XVIII (1965), 355–388." In Kurt Otto Friedrichs, 375. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5385-3_24.

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Friedrichs, K. O., and P. D. Lax. "[65-1] Boundary value problems for first order operators, (With Peter D. Lax), Comm. Pure Appl. Math., XVIII (1965), 355–388." In Kurt Otto Friedrichs, 375–409. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5379-2_13.

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Morawetz, Cathleen S. "On symmetrizable differential operators, Proc. Symp. Pure Math., 10 (1967), Singular Integrals, ed. Alberto P. Calderon, A.M.S., 128–137, (with P.D. Lax)." In Kurt Otto Friedrichs, 411. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5385-3_27.

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Friedrichs, K. O., and P. D. Lax. "[67-1] On symmetrizable differential operators, Proc. Symp. Pure Math., 10 (1967), Singular Integrals, ed. Alberto P. Calderon, A.M.S., 128–137, (with P.D. Lax)." In Kurt Otto Friedrichs, 411–21. Boston, MA: Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4612-5379-2_14.

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Conference papers on the topic "Lax-Friedrichs"

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Manshoor, Bukhari, Amir Khalid, Azwan Sapit, Izzuddin Zaman, and Akmal Nizam. "Numerical solution of Burger’s equation based on Lax-Friedrichs and Lax-Wendroff schemes." In 7TH INTERNATIONAL CONFERENCE ON MECHANICAL AND MANUFACTURING ENGINEERING: Proceedings of the 7th International Conference on Mechanical and Manufacturing Engineering, Sustainable Energy Towards Global Synergy. Author(s), 2017. http://dx.doi.org/10.1063/1.4981166.

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Yulianti, Kartika, Rini Marwati, and Suci Permatahati. "A Modified Lax-Friedrichs Method for the Shallow Water Equations." In Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia. EAI, 2020. http://dx.doi.org/10.4108/eai.12-10-2019.2296327.

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Ye, Shijie, Yanping Guo, Jianliang Li, and Ming Lu. "Simulation Analysis for Peak Pressure of Shock Wave Based on Lax-Friedrichs Method." In 2012 Fifth International Conference on Information and Computing Science (ICIC). IEEE, 2012. http://dx.doi.org/10.1109/icic.2012.48.

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Feng, Fan, Chunwei Gu, and Xuesong Li. "Discontinuous Galerkin Solution of Three-Dimensional Reynolds-Averaged Navier-Stokes Equations With S-A Turbulence Model." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23133.

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In this paper Discontinuous Galerkin Method (DGM) is applied to solve the Reynolds-averaged Navier-Stokes equations and S-A turbulence model equation in curvilinear coordinate system. Different schemes, including Lax-Friedrichs (LF) flux, Harten, Lax and van Leer (HLL) flux and Roe flux are adopted as numerical flux of inviscid terms at the element interface. The gradients of conservative variables in viscous terms are constructed by mixed formulation, which solves the gradients as auxiliary unknowns to the same order of accuracy as conservative variables. The methodology is validated by simulations of double Mach reflection problem and three-dimensional turbulent flowfield within compressor cascade NACA64. The numerical results agree well with the experimental data.
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Arminjon, P., A. Madrane, and A. St.-Cyr. "New Lax-Friedrichs-type finite volume schemes on 2 and 3D Cartesian staggered grids." In 14th Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-3362.

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Riestiana, V. A., R. Setiyowati, and V. Y. Kurniawan. "Numerical solution of the one dimentional shallow water wave equations using finite difference method : Lax-Friedrichs scheme." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039545.

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Li Zhang, Andy M. Yip, and Chew Lim Tan. "Shape from Shading Based on Lax-Friedrichs Fast Sweeping and Regularization Techniques With Applications to Document Image Restoration." In 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2007. http://dx.doi.org/10.1109/cvpr.2007.383287.

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Herdman, Terry L., and Kyehong Kang. "An Optimization Based Approach to Flow Matching for Burger’s Equation With a Forcing Term." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0681.

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Abstract We consider the use of a numerical optimization technique to solve an inverse problem for Burger’s equation with a periodic forcing term. The solution depends on the initial data profile. The goal is to obtain an optimal continuous linear initial profile which generates the fixed target solution using a numerical optimization technique. Because Burger’s equation is time dependent, the cost function measures the difference between the target and the computed solution at a fixed final time. The optimization algorithm utilizes BFGS updates without computing Hessians and a line search is applied as a globalization. Burger’s equation is solved by a generalized Lax-Friedrichs scheme. This problem is motivated by flow matching problems in optimal design of nozzles and 1-dimensional ducts (see [1]).
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Shang, J. S. "A Glance Back and Outlook of Computational Fluid Dynamics (Keynote Paper)." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45420.

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The development of computational fluid dynamics (CFD) can be traced back as far as the early 1900’s. The pioneering efforts by Richardson [1], Courant, Friedrichs, and Lewy [2], Southwell [3], Von Neumann [4], Lax [5], as well as Godunov [6] address the fundamental issues in numerical analyses for CFD. It is immediately clear that a major portion of these efforts was focused on one of the most difficult problems in resolving the discontinuous fluid phenomena in a discretized space — the Riemann problem [7]. As it will be seen later, it remains the most studied problem in CFD. However, if one is interested in the viscous flow simulation, Thom [8] probably obtained the first-ever numerical solution by solving the partial differential equation for a low speed flow past a circular cylinder. For a scholarly description of the CFD historical perspective, the books by Roach [9] and Tannehill, Anderson, and Pletcher [10] are highly recommended.
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