Asymptotic expansion analysis of nonconforming mixed finite element methods for time-dependent Maxwell's equations in Debye Medium

In this paper, based on our previous work of asymptotic expansion, an initial effort of global superconvergence analysis of time-domain Maxwell's equations in Debye Medium is obtained for semi-discrete mixed finite element scheme. During this procedure, superclose analysis of the interpolation of the smoothing solution and the solution of mixed finite element method is obtained for the fist time. By the post-processing operators, superconvergence phenomena can be found. To our best knowledge, this is the first global superconvergence analysis presented by nonconforming mixed finite element methods when Debye Medium is involved.