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

Published online by Cambridge University Press:  21 February 2011

Snorre H. Christiansen  and
Claire Scheid
Snorre H. Christiansen
Affiliation:
CMA c/o Dept. Math, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway. [email protected]
Claire Scheid
Affiliation:
CMA c/o Dept. Math, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway. [email protected] Laboratoire Jean Alexandre Dieudonné, Université de Nice Sophia Antipolis, 06108 Nice Cedex 02, France. [email protected]
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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.

Keywords

WavesMaxwell Klein Gordonnon-linear constraintsfinite elementsconvergence analysis
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 4 , July 2011 , pp. 739 - 760
Copyright
© EDP Sciences, SMAI, 2011

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