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SIAM J. Numer. Anal. 46, pp. 747-775 (29 pages)
An Optimal Adaptive Finite Element Method for the Stokes Problem
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Add to FacebookA new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems is a Stokes-type problem, with the pressure being sought in the current trial space and the divergence-free constraint being reduced to orthogonality of the divergence to this trial space. Such a problem is still continuous in the velocity field. In the middle loop, its solution is approximated using the Uzawa scheme. In the innermost loop, the solution of the elliptic system for the velocity field that has to be solved in each Uzawa iteration is approximated by an adaptive finite element method.
© 2008 Society for Industrial and Applied Mathematics
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Received July 21, 2006
Accepted July 10, 2007
Published online February 08, 2008
Accepted July 10, 2007
Published online February 08, 2008
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