Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, p. 903-932

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.

DOI : https://doi.org/10.1051/m2an/2012061
Classification:  35L05,  65M12,  65M60
Keywords: discontinuous Galerkin, penalization coefficient, CFL condition, wave equation
@article{M2AN_2013__47_3_903_0,
     author = {Agut, Cyril and Diaz, Julien},
     title = {Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {3},
     year = {2013},
     pages = {903-932},
     doi = {10.1051/m2an/2012061},
     zbl = {1266.65151},
     mrnumber = {3056414},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_3_903_0}
}
Agut, Cyril; Diaz, Julien. Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, pp. 903-932. doi : 10.1051/m2an/2012061. http://www.numdam.org/item/M2AN_2013__47_3_903_0/

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