Adaptive Uzawa algorithm for the Stokes equation

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.

References in corpus (1)

• Adaptive BEM with inexact PCG solver yields almost optimal computational costs

Cited by in corpus (2)

• Mathematical foundations of adaptive isogeometric analysis
• Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver