A Mixed Finite Element Method for the Contact Problem in Elasticity

Abstract

Based on the analysis of [7] and [10], we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from $\mathcal{O}(h^{3/4})$ to quasi-optimal $\mathcal{O}(h|logh|^{1/4})$. If stronger but reasonable regularity is available, the convergence rate can be optimal $\mathcal{O}(h)$.