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Wavelet preconditioning of the Stokes problem in ψ–ω formulation

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Abstract

The diagonal preconditioning in wavelet basis enables one to obtain an optimal preconditioner for Galerkin discretizations of elliptic operators in Sobolev norms of both positive and negative smoothness. We develop these techniques in order to solve efficiently the bi-Laplacian or the bidimensional Stokes problem in ψ–ω formulation using a diagonal preconditioning in wavelet basis for the H−1/2(∂Ω) boundary operator that relates the trace of ∂nψ to the trace of ω.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, tour 55-65, 5ème étage, 4 place Jussieu, F-75252, Paris Cedex 05, France

    Pascal Joly

  2. Département Informatique Scientifique et Mathématiques Appliquées, Institut Français du Pétrole, F-92500, Rueil Malmaison Cedex, France

    Roland Masson

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  1. Pascal Joly
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  2. Roland Masson
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Joly, P., Masson, R. Wavelet preconditioning of the Stokes problem in ψ–ω formulation. Numerical Algorithms 24, 357–369 (2000). https://doi.org/10.1023/A:1019165831641

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