Analysis Of Nonconforming Finite Element For Two Kinds Of Equations

In this paper, ACM nonconforming finite element approximation to nonlinear fourth-order hyperbolic equation is first discussed for semi-discrete scheme. The optimal order error estimates, superclose and superconvergence are derived. At the same time, by virtue of the Bramble-Hilbert lemma, we construct a new and suitable extrapolation scheme and obtain a superconvergence result which is one order higher than the usual convergence.Then we consider the convergence analysis of nonconforming finite element for the time dependent Maxwell’s equations resulting from Debye medium model. On the one hand, a nonconforming mixed finite element scheme is introduced, and a character of the consistency error which is one order higher than interpolation error in sense of H1norm is proved based on the matching property of the mixed element and the constructions of some special interpolation operators. On the other hand, the convergence analysis and the error estimation of L2norm for the semi discrete and fully discrete of explicit leap-frog form are devived under a perfect conducting boundary condition, in which the explicit constants in the error estimates are given, which have never been studied in the previous literature.