WIAS Preprint No. 1261, (2007)

Non-nested multi-grid solvers for mixed divergence-free Scott--Vogelius discretizations



Authors

  • Linke, Alexander
    ORCID: 0000-0002-0165-2698
  • Matthies, Gunar
  • Tobiska, Lutz

2010 Mathematics Subject Classification

  • 76D05 65F10

2008 Physics and Astronomy Classification Scheme

  • 47.11.-j

Keywords

  • Non-Nested Multi-Grid, Stabilized Finite Elements, Navier-Stokes Equations, LBB-Stability

Abstract

We apply the general framework developed by John et al. in V. John, P. Knobloch, G. Matthies, L. Tobiska: Non-nested multi-level solvers for finite element discretisations of mixed problems, Computing 2002, 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-Babuška-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.

Appeared in

  • Computing, 83 (2008) pp. 87--107.

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