Nonconforming Finite Element Analysis For Two Classes Of Evolution Differential Equations

In this paper, firstly, a new anisotropic nonconforming mixed finite element scheme for solving Sobolev equations is proposed. Under the semi-discrete scheme, the corresponding convergence analysis is presented and the error estimates are obtained by use of the interpolation operator instead of the conventional Ritz-Volterra projection. By virture of the mean value technique and some special features of the element, the superclose and pointwise superconvergence are derived. Secondly, we present the new triangular element (Quasi-Carey element) for approximating the quasi-linearity viscoelasticity equations under the semi-discrete scheme. Based on the mean value estimate technique and some novel approaches of the element, the superclose properties are presented. In addition, the global superconvergence property is derived by the post-processing procedure.