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.

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 : 10.1051/m2an/2012061
Classification : 35L05, 65M12, 65M60
Mots-clés : discontinuous Galerkin, penalization coefficient, CFL condition, wave equation 
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     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},
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     zbl = {1266.65151},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2012061/}
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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. http://www.numdam.org/articles/10.1051/m2an/2012061/

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