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A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes

Published online by Cambridge University Press:  12 August 2008

Malte Braack
Malte Braack*
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany. braack@math.uni-kiel.de
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Abstract

It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instancestreamline upwind Petrov-Galerkin (SUPG), are optimal on isotropicmeshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. Wedescribe the new methodand prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior than other isotropicstabilization methods.The capability of the methodis illustrated by means of two numerical test problems.

Keywords

Incompressible flowNavier-Stokes equationsstabilized finiteelementsanisotropic meshes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 6 , November 2008 , pp. 903 - 924
Copyright
© EDP Sciences, SMAI, 2008

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