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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.
@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 },
pages = {903--932},
publisher = {EDP-Sciences},
volume = {47},
number = {3},
year = {2013},
doi = {10.1051/m2an/2012061},
mrnumber = {3056414},
zbl = {1266.65151},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012061/}
}
TY - JOUR AU - Agut, Cyril AU - Diaz, Julien TI - Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 903 EP - 932 VL - 47 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012061/ DO - 10.1051/m2an/2012061 LA - en ID - M2AN_2013__47_3_903_0 ER -
%0 Journal Article %A Agut, Cyril %A Diaz, Julien %T Stability analysis of the Interior Penalty Discontinuous Galerkin method for the wave equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 903-932 %V 47 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012061/ %R 10.1051/m2an/2012061 %G en %F 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 , Tome 47 (2013) no. 3, pp. 903-932. doi: 10.1051/m2an/2012061
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