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

Zhiqiang Cai

doi:10.1016/S0045-7825(98)00086-3

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

1998-11-01

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DOI：10.1016/S0045-7825(98)00086-3

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This paper studies it 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. It will be shown that the preconditioned conjugate gradient method and other existing iterative approaches can be applied with a convergence rate uniform in the number of unknowns. Also, modifications of other stabilized finite element methods are considered. (C) 1998 Elsevier Science S.A. All rights reserved.

Keywords:

COMPUTATIONAL FLUID-DYNAMICS

LEAST-SQUARES

FORMULATION

EQUATIONS

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

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