Stabilized finite element methods with fast iterative solution algorithms for the Stokes problem

摘要

This paper studies a new absolutely stabilized formulation for the Stokes problem that is a modification of the method of [13]. It is shown that the bilinear form is elliptic and continuous with respect to the H~1 -norm for the velocity and the L~2-norm for the pressure. Optimal order error estimates for the finite element approximation of both the velocity and pressure in L~2 are established, as well as one in H~1 for the velocity. The formulation is nonsymmetric. We then introduce two symmetrized forms which retain ellipticity and continuity with respect to the same norm.