MIXED HP FINITE-ELEMENT METHODS FOR PROBLEMS IN ELASTICITY AND STOKES-FLOW

We consider the mixed formulation for the elasticity problem and the l imiting Stokes problem in R(d), d = 2, 3, We derive a set of sufficien t conditions under which families of mixed finite element spaces are s imultaneously 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( epsilon)) in the displacement/velocity and up to O(k(d-1/2+epsilon)) i n the ''pressure'', with epsilon > 0 arbitrary (both rates being optim al with respect to h). Several choices of elements are discussed with reference to properties desirable in the context of the hp-version.