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Title: A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation
Authors: Ahmed, NaveedBarrenechea, Gabriel R.Burman, ErikGuzmán, JohnnyLinke, AlexanderMerdon, Christian
Publishers version: https://doi.org/10.20347/WIAS.PREPRINT.2740
URI: https://oa.tib.eu/renate/handle/123456789/9390
https://doi.org/10.34657/8428
Other version: https://doi.org/10.1137/20M1351230
Issue Date: 2020
Journal: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik
Volume: 2740
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: Discretization of Navier--Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(hk+1/2) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.
Keywords: incompressible Navier--Stokes equations; divergence-free mixed finite element methods; pressure-robustness; convection stabilization; Galerkin least squares; vorticity equation
Type: report; Text
Publishing status: publishedVersion
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
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Ahmed, Naveed, Gabriel R. Barrenechea, Erik Burman, Johnny Guzmán, Alexander Linke and Christian Merdon, 2020. A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Ahmed, N., Barrenechea, G. R., Burman, E., Guzmán, J., Linke, A. and Merdon, C. (2020) A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. doi: https://doi.org/10.20347/WIAS.PREPRINT.2740.
Ahmed N, Barrenechea G R, Burman E, Guzmán J, Linke A, Merdon C. A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation. Vol. 2740. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2020.
Ahmed, N., Barrenechea, G. R., Burman, E., Guzmán, J., Linke, A., & Merdon, C. (2020). A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation (Version publishedVersion, Vol. 2740). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org/https://doi.org/10.20347/WIAS.PREPRINT.2740
Ahmed N, Barrenechea G R, Burman E, Guzmán J, Linke A, Merdon C. A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation. Vol. 2740. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik; 2020. doi:https://doi.org/10.20347/WIAS.PREPRINT.2740


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