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: 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 },
pages = {739--760},
year = {2011},
publisher = {EDP Sciences},
volume = {45},
number = {4},
doi = {10.1051/m2an/2010100},
mrnumber = {2804657},
zbl = {1282.78036},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2010100/}
}
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 PY - 2011 SP - 739 EP - 760 VL - 45 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2010100/ DO - 10.1051/m2an/2010100 LA - en ID - M2AN_2011__45_4_739_0 ER -
%0 Journal Article %A Christiansen, Snorre H. %A Scheid, Claire %T Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 739-760 %V 45 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2010100/ %R 10.1051/m2an/2010100 %G en %F 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 , Tome 45 (2011) no. 4, pp. 739-760. doi: 10.1051/m2an/2010100
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