| Issue |
ESAIM: M2AN
Volume 53, Number 6, November-December 2019
|
|
|---|---|---|
| Page(s) | 1841 - 1870 | |
| DOI | https://doi.org/10.1051/m2an/2019039 | |
| Published online | 18 October 2019 | |
Adaptive Uzawa algorithm for the Stokes equation
1
TU Wien, Institute for Analysis and Scientific Computing, Wiedner Hauptstr. 8–10/E101/4, 1040 Wien, Austria
2
Pontificia Universidad Católica de Chile, Facultad de Matemáticas, Vickuña Mackenna, 4860 Santiago, Chile
* Corresponding author: gregor.gantner@asc.tuwien.ac.at
Received:
20
December
2018
Accepted:
24
May
2019
Based on the Uzawa algorithm, we consider an adaptive finite element method for the Stokes system. We prove linear convergence with optimal algebraic rates for the residual estimator (which is equivalent to the total error), if the arising linear systems are solved iteratively, e.g., by PCG. Our analysis avoids the use of discrete efficiency of the 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.
Mathematics Subject Classification: 65N30 / 65N50 / 65N15 / 41A25
Key words: Adaptive finite element method / optimal convergence / Uzawa algorithm / Stokes equation
© EDP Sciences, SMAI 2019
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