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

Snorre H. Christiansen (1) , Claire Scheid (2, 3)

1 CMA - Center of Mathematics for Applications [Oslo]
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media

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.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Snorre H. Christiansen, Claire Scheid. Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation.. ESAIM: Mathematical Modelling and Numerical Analysis, 2011, 45 (4), pp.739-760. ⟨10.1051/m2an/2010100⟩. ⟨hal-00874735⟩