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An adaptive stabilized finite element method for the generalized Stokes problem

Araya, R. and Barrenechea, G.R. and Poza, A. (2008) An adaptive stabilized finite element method for the generalized Stokes problem. Journal of Computational and Applied Mathematics, 214 (2). pp. 457-479. ISSN 0377-0427

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In this work we present an adaptive strategy (based on an a posteriori error estimator) for a stabilized finite element method for the Stokes problem, with and without a reaction term. The hierarchical type estimator is based on the solution of local problems posed on appropriate finite dimensional spaces of bubble-like functions. An equivalence result between the norm of the finite element error and the estimator is given, where the dependence of the constants on the physics of the problem is explicited. Several numerical results confirming both the theoretical results and the good performance of the estimator are given.