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Non-Nested Multi-Grid Solvers for Mixed Divergence-free Scott-Vogelius Discretizations

Please always quote using this URN:urn:nbn:de:0296-matheon-4251
  • We apply the general framework developed by John et al. in [15] to analyze the convergence of multi-level methods for mixed finite element discretizations of the generalized Stokes problem using the Scott-Vogelius element. Having in mind that semi-implicit operator splitting schemes for the Navier-Stokes equations lead to this class of problems, we take symmetric stabilization operators into account. The use of the class of Scott-Vogelius elements seems to be promising since discretely divergence-free functions are pointwise divergence-free. However, to satisfy the Ladyzhenskaya-Babuska-Brezzi stability condition, we have to deal in the multi-grid analysis with non-nested families of meshes which are derived from nested macro element triangulations.

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Metadaten
Author:Alexander Linke, Gunar Matthies, Lutz Tobiska
URN:urn:nbn:de:0296-matheon-4251
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/11/14
Release Date:2007/10/31
Tag:
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Dxx Incompressible viscous fluids / 76D05 Navier-Stokes equations [See also 35Q30]
Preprint Number:416
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