Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation

International audienceThe Interior Penalty Discontinuous Galerkin Method (IPDGM) is probably one of the the most efficient Discontinuous Galerkin method for solving the wave equation. However, the appropriate determination of the penalization parameter is still an issue, since a too low value leads to unconditionnaly unstable schemes while a too large value severely hampers the CFL condition of the scheme. In the first part of the talk, we show how to determine the penalization parameter in the case of cartesian meshes and we propose an analytical expression of the CFL condition with respect to this parameter. Then, we consider the case of triangular meshes, for which it is not possible to obtain an analytic expression of the penalization parameter. We show, thanks to a numerical study, that it should rather be expressed as a function of the radius of the inscribed circle of the triangles rather than of the radius of the circumscribed circle. Moreover, we propose more accurate expressions based on the angles of the triangles. Finally, we analyze the influence of these different expressions on the CFL condition of the scheme