Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation*
CMA c/o Dept. Math, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway. email@example.com
2 Laboratoire Jean Alexandre Dieudonné, Université de Nice Sophia Antipolis, 06108 Nice Cedex 02, France. Claire.Scheid@unice.fr
Revised: 21 May 2010
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.
Mathematics Subject Classification: 65M60 / 78M10
Key words: Waves / Maxwell Klein Gordon / non-linear constraints / finite elements / convergence analysis
This work, conducted as part of the award “Numerical analysis and simulations of geometric wave equations” made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme, was supported by funds from the Participating Organizations of EURYI and the EC Sixth Framework Program.
© EDP Sciences, SMAI, 2011