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Space-Time Discontinuous Galerkin Methods for Weak Solutions of Hyperbolic Linear Symmetric Friedrichs Systems [PDF]
Journal of Scientific Computing, 2022 AbstractWe study weak solutions and its approximation of hyperbolic linear symmetric Friedrichs systems describing acoustic, elastic, or electro-magnetic waves. For the corresponding first-order systems we construct discontinuous Galerkin discretizations in space and time with full upwind, and we show primal and dual consistency.
Daniele Corallo +2 more
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The correct use of the Lax–Friedrichs method [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2004 The authors analyze the basic phenomena which may arise by the naive use of the Lax-Friedrichs scheme in 1D. They employ a virtually infinite grid, and as a motivation a simple linear model problem is used for their discussion. They also discuss the effects of the discretizations of a finite computational domain with boundary conditions on the ...
Michael Breuß
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The use of classical Lax–Friedrichs Riemann solvers with discontinuous Galerkin methods [PDF]
International Journal for Numerical Methods in Fluids, 2002 AbstractWhile conducting a von Neumann stability analysis of discontinuous Galerkin methods we discovered that the classic Lax–Friedrichs Riemann solver is unstable for all time‐step sizes. We describe a simple modification of the Riemann solver's dissipation returns the method to stability.
William J. Rider, Robert B. Lowrie
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On the Discontinuous Galerkin Method for Friedrichs Systems in Graph Spaces [PDF]
, 2006 Solutions of Friedrichs systems are in general not of Sobolev regularity and may possess discontinuities along the characteristics of the differential operator. We state a setting in which the well-posedness of Friedrichs systems on polyhedral domains is ensured, while still allowing changes in the inertial type of the boundary.
Max Jensen
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A method for relaxing the Courant-Friedrich-Levy condition in time-explicit schemes [PDF]
Astronomy & Astrophysics, 2005 We present a method for relaxing the Courant-Friedrich-Levy (CFL) condition, which limits the time step size in explicit numerical methods in computational fluid dynamics. The method is based on re-formulating explicit methods in matrix form. Here an explicit method appears as a special case in which the global matrix of coefficients is replaced by the
A. Hujeirat
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Discontinuous Galerkin methods for Friedrichs systems with irregular solutions [PDF]
, 2004 This work is concerned with the numerical solution of Friedrichs systems by discontinuous Galerkin finite element methods (DGFEMs). Friedrichs systems are boundary value problems with symmetric, positive, linear first-order partial differential operators and allow the unified treatment of a wide range of elliptic, parabolic, hyperbolic and mixed-type ...
Max Jensen
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A continuous finite element method with face penalty to approximate Friedrichs' systems [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2007 The authors generalize the face penalty technique of \textit{E. Burman} [SIAM J. Numer. Anal. 43, No. 5, 2012--2033 (2005; Zbl 1111.65102)] and of \textit{E. Burman} and \textit{P. Hansbo} [Comput. Methods Appl. Mech. Eng. 193, No. 15--16, 1437--1453 (2004; Zbl 1085.76033)] in order to approximate satisfactorily Friedrichs' systems using continuous ...
Erik Burman, Alexandre Ern
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A Simulation of Shallow Water Wave Equation Using Finite Volume Method: Lax-Friedrichs Scheme
Journal of Physics: Conference Series, 2019 Abstract Long wave propagation above a bottom topography such as tsunami waves can be modeled mathematically by applying shallow water wave equations. The finite volume method was developed to determine the numerical solution of shallow water wave equations.
Ririn Setiyowati, Sumardi Sumardi
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A Modified Lax-Friedrichs Method for the Shallow Water Equations [PDF]
Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia, 2020 Kartika Yulianti +2 more
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Discrete forms of Friedrichs' inequalities in the finite element method [PDF]
RAIRO. Analyse numérique, 1981 Alexander Ženíšek
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