Preprint 2015-02
P. Bringmann, C. Carstensen and C. Merdon
Guaranteed Error Control For The Pseudostress Approximation Of The Stokes Equations.
Abstract: The pseudostress approximation of the Stokes equations rewrites the stationary Stokes equations with pure (but possibly inhomogeneous) Dirichlet boundary conditions as another (equivalent) mixed scheme based on a stress in Hpdivq and the velocity in L2. Any standard mixed nite element function space can be utilized for this mixed formulation, e.g. the Raviart-Thomas discretization which is related to the Crouzeix-Raviart nonconforming nite element scheme in the lowest-order case. The eective and guaranteed a posteriori error control for this nonconforming velocity-oriented discretization can be generalized to the error control of some piecewise quadratic velocity approximation that is related to the discrete pseudostress. The analysis allows for local inf-sup constants which can be chosen in a global partition to improve the estimation. Numerical examples provide strong evidence for an eective and guaranteed error control with very small overestimation factors even for domains with large anisotropy.
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2015-02
22 pp.