New Residual Based Stabilization Method for the Elasticity Problem (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we consider the mixed finite element method (MFEM) of theelasticity problem in two and three dimensions (2D and 3D). We develop a new residualbased stabilization method to overcome the inf-sup difficulty, and use Langrangeelements to approximate the stress and displacement. The new method is unconditionallystable, and its stability can be obtained directly from Céa's lemma. Optimalerror estimates for the $H^1$-norm of the displacement and $H$(div)-norm of the stresscan be obtained at the same time. Numerical results show the excellent stability andaccuracy of the new method.