An accurate local average contact method for nonmatching meshes

Abstract

The present paper deals with linear and quadratic finite element approximations of the two and three-dimensional unilateral contact problems between two elastic bodies with nonmatching meshes. We propose a simple noninterpenetration condition on the displacements which is local as the well known node-to-segment and node-to-face conditions and accurate like the mortar approach. This condition consists of averaging locally on a few elements the noninterpenetration. We prove optimal convergence rates in 2D and 3D using various linear and quadratic elements. The Taylor patch test and the Hertzian contact test illustrate the theoretical results and show the capabilities of the method.