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A stabilized finite-element method for the Stokes problem including element and edge residuals. (English) Zbl 1109.65097

The authors propose a new stabilized finite element method for the Stokes problem. The method is of a Douglas-Wang type, and includes a positive jump term controlling the residual of the Cauchy stress tensor on the internal edges of the triangulation. A priori error estimates are obtained in the natural norms of the unknowns and an a posteriori error estimator is proposed, analyzed and tested through numerical experiments.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs

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