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Wavelet preconditioning of the Stokes problem in (psgr, ohgr) formulation

Pascal JolyContact Information and Roland MassonContact Information

(1)  Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, tour 55-65, 5ème étage, 4 place Jussieu, F-75252 Paris Cedex 05, France
(2)  Département Informatique Scientifique et Mathématiques Appliquées, Institut Français du Pétrole, F-92500 Rueil Malmaison Cedex, France

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 (psgr, ohgr) formulation using a diagonal preconditioning in wavelet basis for the H1/2(part OHgr) boundary operator that relates the trace of partn psgr to the trace of ohgr.

psi-omega - wavelets - multilevel preconditioners - negative smoothness - elliptic operators - 42C15 - 65N55

This revised version was published online in June 2006 with corrections to the Cover Date.

Contact Information Pascal Joly

Contact Information Roland Masson


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