Vorticity-velocity-pressure formulation for Stokes problem

Amara, M.; Chacón Vera, E.; Trujillo, D.

doi:10.1090/S0025-5718-03-01615-6

Vorticity-velocity-pressure formulation for Stokes problem
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by M. Amara, E. Chacón Vera and D. Trujillo PDF

Math. Comp. 73 (2004), 1673-1697 Request permission

Abstract:

We propose a three-field formulation for efficiently solving a two-dimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered boundary value problem via a mixed-type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the Lagrange multiplier. The obtained formulation is then discretized and a convergence analysis is performed. A priori error estimates are established, and some numerical results are presented to highlight the perfomance of the proposed computational methodology.

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