Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, p. 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 : https://doi.org/10.1051/m2an/2010100
Classification:  65M60,  78M10
Keywords: waves, Maxwell Klein Gordon, non-linear constraints, finite elements, convergence analysis
@article{M2AN_2011__45_4_739_0,
     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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {4},
     year = {2011},
     pages = {739-760},
     doi = {10.1051/m2an/2010100},
     zbl = {1282.78036},
     mrnumber = {2804657},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_4_739_0}
}
Christiansen, Snorre H.; 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, Volume 45 (2011) no. 4, pp. 739-760. doi : 10.1051/m2an/2010100. http://www.numdam.org/item/M2AN_2011__45_4_739_0/

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