Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations

Ludovic Moya

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2012)

  • Volume: 46, Issue: 5, page 1225-1246
  • ISSN: 0764-583X

Abstract

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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

How to cite

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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 46.5 (2012): 1225-1246. <http://eudml.org/doc/273261>.

@article{Moya2012,
abstract = {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},
author = {Moya, Ludovic},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {temporal convergence; discontinuous Galerkin method; time-domain Maxwell equations; component splitting; order reduction},
language = {eng},
number = {5},
pages = {1225-1246},
publisher = {EDP-Sciences},
title = {Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell’s equations},
url = {http://eudml.org/doc/273261},
volume = {46},
year = {2012},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 5
SP - 1225
EP - 1246
AB - 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
LA - eng
KW - temporal convergence; discontinuous Galerkin method; time-domain Maxwell equations; component splitting; order reduction
UR - http://eudml.org/doc/273261
ER -

References

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