The Gradient Discretisation Method for Linear Advection Problems-Reference-Cited by-同舟云学术

The Gradient Discretisation Method for Linear Advection Problems

Published:2019-10-17 Issue:3 Volume:20 Page:437-458
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Droniou Jérôme¹^ORCID,Eymard Robert²^ORCID,Gallouët Thierry³,Herbin Raphaèle³

Affiliation:

1. School of Mathematics , Monash University , Melbourne , Australia

2. LAMA , Université Gustave Eiffel, UPEM , F-77447 Marne-la-Vallée , France

3. Institut de Mathématiques de Marseille , Aix-Marseille Université , Marseille , France

Abstract

Abstract We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence analysis of various numerical schemes, corresponding to the methods known to be GDMs, such as finite elements (conforming or non-conforming, standard or mass-lumped), finite volumes on rectangular or simplicial grids, and other recent methods developed for general polytopal meshes. The scheme is of centred type, with added linear or non-linear numerical diffusion. We complement the convergence analysis with numerical tests based on the mass-lumped ℙ 1

{\mathbb{P}_{1}}

conforming and non-conforming finite element and on the hybrid finite volume method.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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