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The gradient discretisation method for linear advection problems

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.
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https://hal.archives-ouvertes.fr/hal-02078340
Contributor : Robert Eymard <>
Submitted on : Friday, October 18, 2019 - 7:45:58 AM
Last modification on : Tuesday, March 23, 2021 - 3:10:07 AM
Long-term archiving on: : Sunday, January 19, 2020 - 1:14:02 PM

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  • HAL Id : hal-02078340, version 2
  • ARXIV : 1903.12415

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Jérôme Droniou, Robert Eymard, T. Gallouët, R. Herbin. The gradient discretisation method for linear advection problems. Computational Methods in Applied Mathematics, De Gruyter, 2019. ⟨hal-02078340v2⟩

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