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.
Adaptive Uzawa algorithm for the Stokes equation / Di Fratta, G.; Fuhrer, T.; Gantner, G.; Praetorius, D.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 53:6(2019), pp. 1841-1870. [10.1051/m2an/2019039]
Adaptive Uzawa algorithm for the Stokes equation
Di Fratta G.;
2019
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
