Wavelet stabilization and preconditioning for domain decomposition

The aim of this paper is to propose a stabilization technique in order to circumvent the two inf–sup conditions needed for stability of the discretization of the three fields formulation for domain decomposition methods (following the work of Brezzi & Marini (1993) Optimisation et Controle 89–96...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2000-10, Vol.20 (4), p.533-559
Main Authors: Bertoluzza, Silvia, Kunoth, Angela
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fourier analysis
Functional analysis
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
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Summary:The aim of this paper is to propose a stabilization technique in order to circumvent the two inf–sup conditions needed for stability of the discretization of the three fields formulation for domain decomposition methods (following the work of Brezzi & Marini (1993) Optimisation et Controle 89–96). Realization of this technique in terms of wavelets is presented. Furthermore, the resulting discrete problem is shown to admit an asymptotically optimal preconditioner also based on wavelets.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/20.4.533