Back to Search
Start Over
DIVERGENCE-FREE RECONSTRUCTION OPERATORS FOR PRESSURE-ROBUST STOKES DISCRETIZATIONS WITH CONTINUOUS PRESSURE FINITE ELEMENTS.
- Source :
-
SIAM Journal on Numerical Analysis . 2017, Vol. 55 Issue 3, p1291-1314. 24p. - Publication Year :
- 2017
-
Abstract
- Classical inf-sup stable mixed finite elements for the incompressible (Navier-)Stokes equations are not pressure-robust, i.e., their velocity errors depend on the continuous pressure. However, a modification only in the right-hand side of a Stokes discretization is able to reestablish pressure-robustness, as shown recently for several inf-sup stable Stokes elements with discontinuous discrete pressures. In this contribution, this idea is extended to low and high order Taylor-Hood and mini elements, which have continuous discrete pressures. For the modification of the righthand side a velocity reconstruction operator is constructed that maps discretely divergence-free test functions to exactly divergence-free ones. The reconstruction is based on local H(div)-conforming ux equilibration on vertex patches, and fulfills certain orthogonality properties to provide consistency and optimal a priori error estimates. Numerical examples for the incompressible Stokes and Navier- Stokes equations confirm that the new pressure-robust Taylor{Hood and mini elements converge with optimal order and outperform significantly the classical versions of those elements when the continuous pressure is comparably large. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 55
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 123922183
- Full Text :
- https://doi.org/10.1137/16M1089964