Mixed hp finiteelement methods for problems in elasticity and Stokes flow

Summary. We consider the mixed formulation for the elasticity problem and the limiting Stokes problem in , . We derive a set of sufficient conditions under which families of mixed finite element spaces are simultaneously stable with respect to the mesh size and, subject to a maximum loss of , with respect to the polynomial degree . We obtain asymptotic rates of convergence that are optimal up to in the displacement/velocity and up to in the "pressure", with arbitrary (both rates being optimal with respect to ). Several choices of elements are discussed with reference to properties desirable in the context of the -version. Received March 4, 1994 / Revised version received February 12, 1995