Calculus of Variations and Geometric Measure Theory

G. Di Fratta - T. F├╝hrer - G. Gantner - D. Praetorius

Adaptive Uzawa algorithm for the Stokes equation

created by difratta on 30 Apr 2021



Inserted: 30 apr 2021

Year: 2018

ArXiv: 1812.11798 PDF


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.