Optimal adaptivity for a standard finite element method for the Stokes problem

2017/10/20 by Michael Feischl, Feischl, Michael
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1710.08289

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 LU-factorizations of infinite matrices.

Citations

• Optimal adaptive nonconforming FEM for the Stokes problem

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