Trefftz discontinuous Galerkin method for Friedrichs systems with linear relaxation: application to the P 1 model [PDF]
Computational Methods in Applied Mathematics, 2018 Abstract This work deals with the first Trefftz Discontinuous Galerkin (TDG) scheme for a model problem of transport with relaxation. The model problem is written as a P N
Guillaume Morel +2 more
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Discontinuous Galerkin Methods for Friedrichs’ Systems. Part II. Second‐order Elliptic PDEs [PDF]
SIAM Journal on Numerical Analysis, 2006 This paper is the second part of a work attempting to give a unified analysis of discontinuous Galerkin methods. The setting under scrutiny is that of Friedrichs’ systems endowed with a particular $2 \times 2$ structure in which one unknown can be eliminated to yield a system of second-order elliptic-like PDEs for the remaining unknown.
Alexandre Ern, Jean‐Luc Guermond
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On the Poincaré-Friedrichs inequality for piecewise $H^\{1\}$ functions in anisotropic discontinuous Galerkin finite element methods [PDF]
Mathematics of Computation, 2010 The purpose of this paper is to propose a proof for the Poincare-Friedrichs inequality for piecewise H 1 functions on anisotropic meshes. By verifying suitable assumptions involved in the newly proposed proof, we show that the Poincare-Friedrichs inequality for piecewise H 1 functions holds independently of the aspect ratio which characterizes the ...
Huoyuan Duan, Roger C. E. Tan
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Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multifield Theories with Partial Coercivity [PDF]
SIAM Journal on Numerical Analysis, 2008 This paper is the third and last part of a work attempting to give a unified analysis of discontinuous Galerkin methods. The purpose of this paper is to extend the framework that has been developed in Part II for two-field Friedrichs' systems associated with second-order PDEs.
Alexandre Ern, Jean‐Luc Guermond
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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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TDG method for Friedrichs systems and the P N model in 2D [PDF]
, 2019 The recent advances about the construction of a Trefftz Discontinuous Galerkin (TDG) method to a class of Friedrichs systems coming from linear transport with relaxation are presented in a comprehensive setting. Application to the 2D P N model are discussed , together with the derivation of new high order convergence estimates and new numerical results
Christophe Buet +2 more
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arXiv.orgA new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a high order correction to the Lax-Friedrich's method while utilizing a novel cutoff to preserve the convergence ...
Lewis, T., Xue, X.
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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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Discrete forms of Friedrichs' inequalities in the finite element method [PDF]
RAIRO. Analyse numérique, 1981 Alexander Ženíšek
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The Friedrich Microkjeldahl Method for Nitrogen [PDF]
Journal of AOAC INTERNATIONAL, 1950 G. E. Secor +3 more
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