Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, p. 1225-1246

In this paper we study the temporal convergence of a locally implicit discontinuous Galerkin method for the time-domain Maxwell's equations modeling electromagnetic waves propagation. Particularly, we wonder whether the method retains its second-order ordinary differential equation (ODE) convergence under stable simultaneous space-time grid refinement towards the true partial differential equation (PDE) solution. This is not a priori clear due to the component splitting which can introduce order reduction

DOI : https://doi.org/10.1051/m2an/2012002
Classification:  65M12,  65M60,  78M10
Keywords: temporal convergence, discontinuous Galerkin method, time-domain Maxwell equations, component splitting, order reduction
@article{M2AN_2012__46_5_1225_0,
     author = {Moya, Ludovic},
     title = {Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {5},
     year = {2012},
     pages = {1225-1246},
     doi = {10.1051/m2an/2012002},
     zbl = {1277.78036},
     mrnumber = {2916379},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2012__46_5_1225_0}
}
Moya, Ludovic. Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, pp. 1225-1246. doi : 10.1051/m2an/2012002. http://www.numdam.org/item/M2AN_2012__46_5_1225_0/

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