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Vorticity-velocity-pressure formulation for Stokes problem

Authors: M. Amara, E. Chacón Vera and D. Trujillo
Journal: Math. Comp. 73 (2004), 1673-1697
MSC (2000): Primary 65N12; Secondary 35Q30
Published electronically: October 27, 2003
MathSciNet review: 2059731
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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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Additional Information

M. Amara
Affiliation: IPRA-LMA, Université de Pau, 64000 Pau, France

E. Chacón Vera
Affiliation: IPRA-LMA, Université de Pau, 64000 Pau, France

D. Trujillo
Affiliation: Departamento de Ecuaciones Diferenciales y Análisis, Universidad de Sevilla, 41080 Sevilla, Spain

Received by editor(s): January 10, 2002
Received by editor(s) in revised form: March 5, 2003
Published electronically: October 27, 2003
Article copyright: © Copyright 2003 American Mathematical Society