Galerkin finite element methods for the generalized Klein-Gordon-Zakharov equations

In this paper, we propose Galerkin finite element methods to investigate the evolution of the generalized Klein-Gordon-Zakharov equations. The spatial discretization is based on Galerkin finite element method. The combination of time-splitting method and finite difference method is used for temporal discretization. The accuracy and efficiency of our numerical schemes are verified by the error norms, conservation laws and the application in nonrelativistic limit regime and in three spatial dimension of different numerical experiments.