DGM, an item of GDM

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

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

We show that a version of the Discontinuous Galerkin Method (DGM) can be included in the Gradient Discretisation Method (GDM) framework. We prove that it meets the main mathematical gradient discretisation properties on any kind of polytopal mesh, and that it is identical to the Symmetric Interior Penalty Galerkin (SIPG) method in the case of first order polynomials. A numerical study shows the effect of the numerical parameter included in the scheme.

Mots clés: Gradient Discretisation method; Discontinuous Galerkin method

Domaines: Analyse numérique [math.NA]

Robert Eymard, Cindy Guichard. DGM, an item of GDM. FVCA 2017 - International Conference on Finite Volumes for Complex Applications VIII, 2017, Lille, France. ⟨hal-01442922⟩