Optimal adaptivity for a standard finite element method for the Stokes problem
Numerical Analysis
2019-03-20 v2
Abstract
We prove that the a standard adaptive algorithm for the Taylor-Hood discretization of the stationary Stokes problem converges with optimal rate. This is done by developing an abstract framework for indefinite problems which allows us to prove general quasi-orthogonality proposed in [Carstensen et al., 2014]. This property is the main obstacle towards the optimality proof and therefore is the main focus of this work. The key ingredient is a new connection between the mentioned quasi-orthogonality and -factorizations of infinite matrices.
Cite
@article{arxiv.1710.08289,
title = {Optimal adaptivity for a standard finite element method for the Stokes problem},
author = {Michael Feischl},
journal= {arXiv preprint arXiv:1710.08289},
year = {2019}
}
Comments
Updated version after Paper has been accepted. arXiv admin note: text overlap with arXiv:1710.06082