Mixed hp Finite Element Methods for Problems in Elasticity and Stokes Flow

摘要

We consider the mixed formulation for the elasticity problem and the limitingStokes problem. We derive a set of sufficient conditions under which families of mixed finite element spaces are simultaneously stable with respect to the mesh size h and subject to a maximum loss with respect to the polynomial degree k. We obtain asymptotic rates of convergence that are optimal in the displacement/velocity and in the pressure. Several choices of elements are discussed with reference to properties desirable in the context of the hp-version.