Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 4, pp. 739-760.

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.

DOI : 10.1051/m2an/2010100
Classification : 65M60, 78M10
Mots clés : waves, Maxwell Klein Gordon, non-linear constraints, finite elements, convergence analysis
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     author = {Christiansen, Snorre H. and Scheid, Claire},
     title = {Convergence of a constrained finite element discretization of the {Maxwell} {Klein} {Gordon} equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {739--760},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2010100/}
}
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Christiansen, Snorre H.; Scheid, Claire. Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 4, pp. 739-760. doi : 10.1051/m2an/2010100. http://www.numdam.org/articles/10.1051/m2an/2010100/

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