New Residual Based Stabilization Method for the Elasticity Problem

Abstract

In this paper, we consider the mixed finite element method (MFEM) of the elasticity problem in two and three dimensions (2D and 3D). We develop a new residual based stabilization method to overcome the inf-sup difficulty, and use Langrange elements to approximate the stress and displacement. The new method is unconditionally stable, and its stability can be obtained directly from Céa's lemma. Optimal error estimates for the $H^1$-norm of the displacement and $H$(div)-norm of the stress can be obtained at the same time. Numerical results show the excellent stability and accuracy of the new method.