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.
Accepté le :
DOI : 10.1051/m2an/2019039
Mots-clés : Adaptive finite element method, optimal convergence, Uzawa algorithm, Stokes equation
@article{M2AN_2019__53_6_1841_0, author = {Di Fratta, Giovanni and F\"uhrer, Thomas and Gantner, Gregor and Praetorius, Dirk}, title = {Adaptive {Uzawa} algorithm for the {Stokes} equation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1841--1870}, publisher = {EDP-Sciences}, volume = {53}, number = {6}, year = {2019}, doi = {10.1051/m2an/2019039}, mrnumber = {4019762}, zbl = {1434.65248}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2019039/} }
TY - JOUR AU - Di Fratta, Giovanni AU - Führer, Thomas AU - Gantner, Gregor AU - Praetorius, Dirk TI - Adaptive Uzawa algorithm for the Stokes equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 1841 EP - 1870 VL - 53 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2019039/ DO - 10.1051/m2an/2019039 LA - en ID - M2AN_2019__53_6_1841_0 ER -
%0 Journal Article %A Di Fratta, Giovanni %A Führer, Thomas %A Gantner, Gregor %A Praetorius, Dirk %T Adaptive Uzawa algorithm for the Stokes equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 1841-1870 %V 53 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2019039/ %R 10.1051/m2an/2019039 %G en %F M2AN_2019__53_6_1841_0
Di Fratta, Giovanni; Führer, Thomas; Gantner, Gregor; Praetorius, Dirk. Adaptive Uzawa algorithm for the Stokes equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1841-1870. doi : 10.1051/m2an/2019039. http://www.numdam.org/articles/10.1051/m2an/2019039/
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