Name
Title | ||
|---|---|---|
Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations with Continuous Pressure Finite Elements. |
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 right-hand 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 flux 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 con firm 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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1089964 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
incompressible Navier-Stokes equations,mixed finite elements,pressure-robustness,exact divergence-free velocity reconstruction,flux equilibration | Compressibility,Discretization,Mathematical optimization,Stokes' law,Vertex (geometry),Mathematical analysis,Orthogonality,Finite element method,Operator (computer programming),Stokes stream function,Mathematics | Journal |
Volume | Issue | ISSN |
55 | 3 | 0036-1429 |
Citations | PageRank | References |
9 | 0.56 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Philip L. Lederer | 1 | 13 | 1.71 |
| Alexander Linke | 2 | 92 | 12.29 |
| Christian Merdon | 3 | 62 | 7.33 |
| Joachim Schöberl | 4 | 213 | 21.63 |