Wavelet bases in \(\mathbf{H}( \text{div})\) and \(\mathbf{H}(\text \textbf{curl})\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0963.65155
DOI: 10.1090/S0025-5718-00-01245-X
author: Karsten Urban
published in: Mathematics of Computation
publication date: 2001-02-19T00:00:00Z
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 1566130
zbMATH Keywords: wavelets
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Stokes equations
zbMATH Keywords: equations of electromagnetic theory
zbMATH Keywords: stream function spaces
zbMATH Keywords: condition numbers
zbMATH Keywords: multilevel preconditioners
MaRDI profile type: Publication
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full work available at URL: s0025-5718-00-01245-x
OpenAlex ID: W2102968800
title: Wavelet bases in \(\mathbf{H}( \text{div})\) and \(\mathbf{H}(\text \textbf{curl})\)
review text: The author constructs stable (biorthogonal) wavelet bases for the stream function spaces \(\mathbf H (\mathbf{curl};\Omega)\). Moreover, \textbf{curl}-free vector wavelets are constructed and analysed. The relationship between \(\mathbf H(\text{div};\Omega)\) and \(\mathbf H(\mathbf {curl};\Omega)\) are expressed in terms of these wavelets. Discrete (orthogonal) Hodge decomposition of \(\mathbf L^2(\Omega)\) is obtained. The author gives examples of domains and wavelet bases fulfilling the general hypothesis and computes \textbf{curl}-free vector wavelets explicitely starting from biorthogonal spline wavelets. Using this decomposition, the author constructs wavelet multilevel preconditioners in \(\mathbf H(\text{div};\Omega)\) and \(\mathbf H(\mathbf {curl};\Omega)\) that give rise to uniformly bounded condition numbers. As an application, wavelet multilevel preconditioners in \(\mathbf H(\text{div};\Omega)\) and \(\mathbf H(\mathbf {curl};\Omega)\) are obtained.
reviewed by: Karel Najzar
description: scientific article