A Class Of Anisotropic Non-conforming Element In The Development Equation

A class of low order nonconforming finite element approximations to evolution equations are discussed in this paper. First, we applied these finite element approximations to hyperbolic intergrodifFerential equations with semidiscretization on anisotropic meshes, the same optimal error estimates and superclose properties as the traditional methods are derived. Furthermore, the global superconvergence are obtained through postprocessing technique. Then, another application to Sobolev equations are discussed. The semidiscretization and discretization formular are studied seperately. The optimal error estimates and superclose properties are obtained as well as the former equations. At the same time, the global superconvergence results are given with the semidiscretization. Finally, the anisotropic property of two nonconforming element are checked, the corresponding numerical examples are given to confirm our analysis.