Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein-Gordon-Schrodinger equations

In this paper, a linearized mass and energy conservative mixed finite element method (MFEM) is proposed for solving the nonlinear Klein-Gordon-Schrodinger equations. Optimal error estimates without grid-ratio condition are derived by some rigorous analysis and an error splitting technique, that is, one is the temporal error which is only tau-dependent and the other is the spatial error which is only h-dependent. Furthermore, the superclose results are obtained by using the idea of combination of interpolation and projection. Besides, a so-called "lifting " approach also play an important role to obtain the superclose results. With the above achievements, the global superconvergent properties are deduced through the interpolated post processing operators. Finally, three numerical examples are given to validate the convergence order, unconditional stability, mass, and energy conservation.