Mixed Hp Nite Element Methods for Problems in Elasticity and Stokes Ow

We consider the mixed formulation for the elasticity problem and the limiting Stokes problem in IR d , d = 2; 3. We derive a set of suucient conditions under which families of mixed nite element spaces are simultaneously stable with respect to the mesh size h and, subject to a maximum loss of O(k d?1 2), with respect to the polynomial degree k. We obtain asymptotic rates of convergence that are optimal up to O(k) in the displacement/velocity and up to O(k d?1 2 +) in the \pressure", with > 0 arbitrary (both rates being optimal with respect to h). Several choices of elements are discussed with reference to properties desirable in the context of the hp-version.