Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation (Q2839132)

The paper is concerned with the numerical analysis of the Maxwell-Klein-Gordon (MKG) equation. The authors prove the convergence in space dimension 2, for initial data of finite energy, of a constraint preserving semi-discrete scheme based on finite elements, introduced by \textit{S. H. Christiansen} [SIAM J. Sci. Comput. 31, No. 2, 1448--1469 (2009; Zbl 1202.65122)]. In the MKG equation the unknowns are the electromagnetic field, described by a vector potential an a scalar complex field. The essential features of the scheme are that it preserves energy, which gives control over the curl of the vector potential, and that the constraint preservation give control over its divergence.