The gradient discretisation method for linear advection problems

Jérôme Droniou, Robert Eymard, Thierry Gallouët, Raphaèle Herbin

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3 Citations (Scopus)

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 ℙ1 conforming and non-conforming finite element and on the hybrid finite volume method.

Original languageEnglish
Number of pages23
JournalComputational Methods in Applied Mathematics
DOIs
Publication statusAccepted/In press - Oct 2019

Keywords

  • Convergence Analysis
  • Gradient Discretisation Method
  • Linear Scalar Hyperbolic Equation
  • Numerical Tests

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