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A stabilized finite-element method for the Stokes problem including element and edge residuals

Araya, Rodolfa and Barrenechea, Gabriel and Valentin, Frédéric (2007) A stabilized finite-element method for the Stokes problem including element and edge residuals. IMA Journal of Numerical Analysis, 27 (1). pp. 172-197. ISSN 0272-4979

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Abstract

A new stabilized finite-element method is presented 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, analysed and tested through numerical experiments.