DGM, an item of GDM

Abstract

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 ssthat 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.