A New Stabilization Method for the Elasticity Problem

In this paper, we consider the elasticity problem based on the Hellinger–Reissner variational principle. We use the C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} continuous arbitrary degree polynomial mixed finite element spaces to approximate the stress and displacement, and develop a new stabilization method for the finite element space pairs to overcome the lack of the inf-sup condition, then we give the corresponding error estimates of the stabilization approximation scheme. At last, we implement a numerical example to test the stability and effectiveness of the proposed method.