Higher Efficient Finite Element Analysis For Strongly Damping Wave Equation And Viscoelasticity Type Equation

This paper includes two parts:In the first part, we focus on higher accuracy analysis for strongly damping wave equation. Firstly, a new rectangular mixed finite element scheme for this equation is proposed based on the bilinear element and zero-order R-T element, which has the advantages:the BB condition is satisfied automatically and the total degrees of freedom involved are lowest etc. The global superclose and superconvergence results are obtained. Secondly, the bilinear element approximation for this equation is studied, the su-perclose and superconvergence results of H1norm are derived by virtue of the known error estimates of the bilinear element and the interpolation post-processing techniques. More-over, the three-order extrapolation solution is achieved through constructing a new and suitable extrapolation scheme. In the second part, we discuss an H1-Galerkin expanded mixed finite element method for viscoelasticity type equation, the optimal approximation of three variables:the unknown function, its gradient and its flux(the gradient multiplies the coefficients) are presented in which the finite element spaces do not need to satisfy the BB condition, the mesh generation need not to be quasi-uniform assumption.