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Title: On the grad-div stabilization for the steady Oseen and Navier-Stokes equations
Authors: Ahmed, Naveed
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2188, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: This paper studies the parameter choice in the grad-div stabilization applied to the generalized problems of Oseen type. Stabilization parameters based on minimizing the H1 (Omega) error of the velocity are derived which do not depend on the viscosity parameter. For the proposed parameter choices, the H1 (Omega) error of the velocity is derived that shows a direct dependence on the viscosity parameter. Differences and common features to the situation for the Stokes equations are discussed. Numerical studies are presented which confirm the theoretical results. Moreover, for the Navier-Stokes equations, numerical simulations were performed on a two-dimensional flow past a circular cylinder. It turns out, for the MINI element, that the best results can be obtained without grad-div stabilization.
Keywords: incompressible Navier–Stokes equations; mixed fnite elements; grad-div stabilization; error estimates; stabilization parameter
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.
Appears in Collections:Mathematik

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