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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
@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 },
pages = {1225--1246},
publisher = {EDP-Sciences},
volume = {46},
number = {5},
year = {2012},
doi = {10.1051/m2an/2012002},
mrnumber = {2916379},
zbl = {1277.78036},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012002/}
}
TY - JOUR AU - Moya, Ludovic TI - Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1225 EP - 1246 VL - 46 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012002/ DO - 10.1051/m2an/2012002 LA - en ID - M2AN_2012__46_5_1225_0 ER -
%0 Journal Article %A Moya, Ludovic %T Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1225-1246 %V 46 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012002/ %R 10.1051/m2an/2012002 %G en %F 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 , Tome 46 (2012) no. 5, pp. 1225-1246. doi: 10.1051/m2an/2012002
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