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

Cyril Agut 1, 2 Julien Diaz 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : We consider here the Interior Penalty Discontinuous Galerkin (IPDG) discretization of the wave equation. We show how to derive the optimal penalization parameter involved in this method in the case of regular meshes. Moreover, we provide necessary stability conditions of the global scheme when IPDG is coupled with the classical Leap-Frog scheme for the time discretization. Numerical experiments illustrate the fact that these conditions are also sufficient.
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Cyril Agut, Julien Diaz. Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2013, 47 (3), pp.903-932. ⟨10.1051/m2an/2012061⟩. ⟨hal-00759457⟩

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