Non-conforming Computational Methods for Mixed Elasticity Problems

In this paper, we present a non-conforming hp computational modeling methodology for solving elasticity problems. We consider the incompressible elasticity model formulated as a mixed displacement-pressure problem on a global domain which is partitioned into several local subdomains. The approximation within each local subdomain is designed using div-stable hp-mixed finite elements. The displacement is computed in a mortared space while the pressure is not subjected to any constraints across the interfaces. Our computational results demonstrate that the non-conforming finite element method presented for the elasticity problem satisfies similar rates of convergence as the conforming finite element method, in the presence of various h- version and p-version discretizations.