The discontinuous Galerkin gradient discretisation

Robert Eymard (1) , Cindy Guichard (2, 3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LJLL - Laboratoire Jacques-Louis Lions
3 ANGE - Numerical Analysis, Geophysics and Ecology

The Symmetric Interior Penalty Galerkin (SIPG) method, based on Discontinuous Galerkin approximations , is shown to be included in the Gradient Discretisation Method (GDM) framework. Therefore, it can take benefit from the general properties of the GDM, since we prove that it meets the main mathematical gradient discretisation properties on any kind of polytopal mesh. For this proof, we adapt discrete functional analysis properties to our precise geometrical hypotheses. We illustrate this inheritance property on the case of the p−Laplace problem. A short numerical study shows the effect of the numerical parameter included in the scheme.

Keywords: Gradient Discretisation method; Discontinuous Galerkin method; Symmetric Interior Penalty Galerkin scheme; discrete functional analysis; polytopal meshes

Domains: Numerical Analysis [math.NA]

Robert Eymard, Cindy Guichard. The discontinuous Galerkin gradient discretisation. 2017. ⟨hal-01535147v1⟩