Adaptive wavelet methods. II: Beyond the elliptic case
type: Item
instance of: scholarly article
title: Adaptive wavelet methods. II: Beyond the elliptic case
zbMATH Open document ID: 1025.65056
author: Wolfgang Dahmen
author: Ronald DeVore
author: Albert Cohen
published in: Foundations of Computational Mathematics
publication date: 2003-11-17T00:00:00Z
review text: [For part I see Math. Comput. 70, 27--75 (2001; Zbl 0980.65130)]. Design and analysis of adaptive wavelet methods for systems of operator equations is presented. The existing theory on adaptive wavelet-based methods is extended from symmetric positive definite problems to indefinite or nonsymmetric systems of operator equations. This is accomplished by introducing techniques (such as the least-squares formulation) that transform the original (continuous problem) into an equivalent infinite system of equations which is now well-posed in the Euclidean metric. For a wide range of problems it is shown that the new adaptive method performs with asymptotically optimal complexity. Furthermore it automatically stabilizes the numerical procedure so that, for instance, compatibility constraints on the choice of spaces, like the Ladyshenskaya-Babuška-Brezzi condition, no longer arise.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 35R20
zbMATH DE Number: 1890496
zbMATH Keywords: wavelets
zbMATH Keywords: adaptive methods
zbMATH Keywords: indefinite problems
zbMATH Keywords: convergence
zbMATH Keywords: quasi-sparse matrices
zbMATH Keywords: stability
zbMATH Keywords: operator equations
zbMATH Keywords: complexity
zbMATH Keywords: Ladyshenkaya-Babuška-Brezzi condition
reviewed by: Wilhelm Heinrichs
Wikidata QID: Q42382622
MaRDI profile type: Publication
full work available at URL: s102080010027
OpenAlex ID: W2048834141
DBLP publication ID: journals/focm/CohenDD02
DOI: 10.1007/S102080010027
description: scientific article; zbMATH DE number 1890496