Stabilized finite elements for transient flow problems on varying spatial meshes.

Braack, Malte, Lang, J. and Taschenberger, N. (2013) Stabilized finite elements for transient flow problems on varying spatial meshes. Computer Methods in Applied Mechanics and Engineering, 253 . pp. 106-116. DOI 10.1016/j.cma.2012.08.006.

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Changing the spatial mesh in transient flow computations may negatively affect the pressure on the new mesh due to the fact that the interpolated or L2L2-projected velocities usually violate the divergence constraint on the new mesh. It is proven that this pressure perturbation scales as k-1k-1 when k denotes the time step. Hence, this phenomenon becomes increasingly relevant for small time steps. This is even more important due to the fact that this phenomena occurs independently whether the discrete scheme is inf-sup stable or not. In order to solve this problem, a divergence free projection should be applied instead of a simple interpolation or L2L2-projection of the velocities. For inf–sup stable finite elements, a recent published analysis shows how such a projection should be performed. For non inf-sup stable finite element pairs with stabilization techniques, as for instance equal-order elements, such an analysis is still missing. In this work, we tackle this problem, present a possible algorithm and prove bounds of the pressure in the linear Stokes case. The type of pressure stabilization is very general and includes the interior penalty method, local projection techniques and others.

Document Type: Article
Additional Information: Times Cited: 0 Braack, Malte Lang, Jens Taschenberger, Nico
Keywords: Stabilized finite elements, Navier–Stokes, Stokes equations, Adaptivity, Divergence free projection
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence
OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
Kiel University
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.1016/j.cma.2012.08.006
ISSN: 0045-7825
Projects: Future Ocean
Date Deposited: 08 Jul 2014 08:54
Last Modified: 23 Sep 2019 17:38

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