Stabilized wavelet approximations of the Stokes problem
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- by Claudio Canuto and Roland Masson PDF
- Math. Comp. 70 (2001), 1397-1416 Request permission
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.References
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Additional Information
- Claudio Canuto
- Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- MR Author ID: 44965
- ORCID: 0000-0002-8481-0312
- 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
- Received by editor(s): June 4, 1999
- Received by editor(s) in revised form: October 18, 1999
- Published electronically: 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 Murst 40% Analisi Numerica.
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1397-1416
- MSC (2000): Primary 65N30, 65N12, 42C15
- DOI: https://doi.org/10.1090/S0025-5718-00-01263-1
- MathSciNet review: 1836910