Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation

Snorre H. Christiansen; Claire Scheid

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2011)

  • Volume: 45, Issue: 4, page 739-760
  • ISSN: 0764-583X

Abstract

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As an example of a simple constrained geometric non-linear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semi-discrete scheme based on finite elements and prove its convergence in space dimension 2 for initial data of finite energy.

How to cite

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Christiansen, Snorre H., and Scheid, Claire. "Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.4 (2011): 739-760. <http://eudml.org/doc/273313>.

@article{Christiansen2011,
abstract = {As an example of a simple constrained geometric non-linear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semi-discrete scheme based on finite elements and prove its convergence in space dimension 2 for initial data of finite energy.},
author = {Christiansen, Snorre H., Scheid, Claire},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {waves; Maxwell Klein Gordon; non-linear constraints; finite elements; convergence analysis; geometric wave equation, Maxwell-Klein-Gordon equation},
language = {eng},
number = {4},
pages = {739-760},
publisher = {EDP-Sciences},
title = {Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation},
url = {http://eudml.org/doc/273313},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Christiansen, Snorre H.
AU - Scheid, Claire
TI - Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 4
SP - 739
EP - 760
AB - As an example of a simple constrained geometric non-linear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semi-discrete scheme based on finite elements and prove its convergence in space dimension 2 for initial data of finite energy.
LA - eng
KW - waves; Maxwell Klein Gordon; non-linear constraints; finite elements; convergence analysis; geometric wave equation, Maxwell-Klein-Gordon equation
UR - http://eudml.org/doc/273313
ER -

References

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