A New Stabilized Scheme Applied to Incompressible Elasticity: A-priori and A-posteriori Analysis

Abstract

We develop an a-priori and an a-posteriori error analysis for a stabilised mixed finite element method applied to incompressible elasticity. The stabilised formulation is obtained by adding to the standard dual-mixed approach suitable least-squares terms arising from the constitutive and equilibrium equations. It is shown that the resulting variational formulation is strongly coercive, which allows to use any pair of finite element subspaces for the corresponding discrete scheme. In particular, Raviart-Thomas spaces of lowest order for the stress tensor and piecewise linear elements for the displacement, can be used. Additionally, we derive a simple a-posteriori error estimator and prove that it is reliable and locally efficient. Finally, we include several numerical experiments that confirm the theoretical results.