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Stabilized wavelet approximations of the Stokes problem

Author(s): Claudio Canuto; Roland Masson.
Journal: Math. Comp. 70 (2001), 1397-1416.
MSC (2000): Primary 65N30, 65N12, 42C15
Posted: July 21, 2000
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Abstract:

We propose a new consistent, residual-based stabilization of the Stokes problem. The stabilizing term involves a pseudo-differential operator, defined via a wavelet expansion of the test pressures. This yields control on the full $L^2$-norm of the resulting approximate pressure independently of any discretization parameter. The method is particularly well suited for being applied within an adaptive discretization strategy. We detail the realization of the stabilizing term through biorthogonal spline wavelets, and we provide some numerical results.

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Additional Information:

Claudio Canuto
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Email: ccanuto@polito.it

Roland Masson
Affiliation: Département Informatique Scientifique et Mathématiques Appliquées, Institut Français du Pétrole, BP 311, 92852 Rueil Malmaison Cedex, France
Email: roland.masson@ifp.fr

DOI: 10.1090/S0025-5718-00-01263-1
PII: S 0025-5718(00)01263-1
Keywords: Stokes problem, inf-sup condition, stabilization, wavelet bases
Received by editor(s): June 4, 1999
Received by editor(s) in revised form: October 18, 1999
Posted: July 21, 2000
Additional Notes: This work was partially supported by the European Commission within the TMR project (Training and Mobility for Researchers) Wavelets and Multiscale Methods in Numerical Analysis and Simulation, No. ERB FMRX CT98 0184, and by the Italian funds {\sc Murst} 40% Analisi Numerica.
Copyright of article: Copyright 2000, American Mathematical Society

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