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G. Di Fratta, T. Führer, G. Gantner, D. Praetorius:
"Adaptive Uzawa algorithm for the Stokes equation";
in: "ASC Report 34/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 29.

Based on the Uzawa algorithm, we consider an adaptive finite element method for the Stokes system. We prove linear convergence with optimal algebraic rates, if the arising linear systems are solved iteratively, e.g., by PCG. Our analysis avoids the use of efficiency estimates for the residual error estimator. Unlike prior work, our adaptive Uzawa algorithm can thus avoid to discretize the given data and does not rely on an interior node property for the refinement.

adaptive finite element method; optimal convergence; Uzawa algorithm; Stokes equation

http://www.asc.tuwien.ac.at/preprint/2018/asc34x2018.pdf