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Article overview
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Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations With Continuous Pressure Finite Elements | Philip L. Lederer
; Alexander Linke
; Christian Merdon
; Joachim Schöberl
; | Date: |
13 Sep 2016 | 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 $H(mathrm{div})$-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 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. | Source: | arXiv, 1609.3701 | Services: | Forum | Review | PDF | Favorites |
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