Energy conserving Galerkin finite element methods for the Maxwell-Klein-Gordon system - Ma, Chupeng; Cao, Liqun; Lin, Yanping (SIAM journal on numerical analysis, 2020)
In this paper, we consider the Galerkin finite element methods for the Maxwell- Klein-Gordon system in the Coulomb gauge. We propose a semidiscrete finite element method for the system with the mixed finite element approximation of the vector potential. Energy conservation and error estimates are established for this scheme. A novel energy conserving time integration scheme is presented for solving the semidiscrete system. The existence and uniqueness of solutions to the fully discrete system are proved under some assumptions. Numerical experiments are carried out to support our theoretical analysis.