Araya, Rodolfo; Barrenechea, Gabriel R.; Valentin, Frédéric A stabilized finite-element method for the Stokes problem including element and edge residuals. (English) Zbl 1109.65097 IMA J. Numer. Anal. 27, No. 1, 172-197 (2007). 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. Reviewer: Răzvan Răducanu (Iaşi) Cited in 6 Documents 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 Keywords:Stokes equation; stabilized method; jump term; finite element method; a priori error estimates; a posteriori error estimator; numerical experiments Software:Triangle PDFBibTeX XMLCite \textit{R. Araya} et al., IMA J. Numer. Anal. 27, No. 1, 172--197 (2007; Zbl 1109.65097) Full Text: DOI