On the construction of stable curvilinear p version elements for mixed formulations of elasticity and Stokes flow

The use of mixed finite element methods is well-established in the numerica l approximation of the problem of nearly incompressible elasticity, and its limit, Stokes flow. The question of stability over curved elements for suc h methods is of particular significance in the p version, where, since the element size remains fixed, exact representation of the curved boundary by (large) elements is often used. We identify a mixed element which we show t o be optimally stable in both p and h, refinement over curvilinear meshes. We prove optimal p version (up to O(p(epsilon))) and h version (p = 2, 3) c onvergence for our element, and illustrate its optimality through numerical experiments. Mathematics Subject Classification (1991): 65N30.