On multi-level bases for elliptic boundary value problems
type: Item
instance of: scholarly article
title: On multi-level bases for elliptic boundary value problems
zbMATH Open document ID: 0862.65063
DOI: 10.1016/0377-0427(95)00214-6
author: Ming-Jun Lai
author: Paul R. Wenston
published in: Journal of Computational and Applied Mathematics
publication date: 1997-05-25T00:00:00Z
review text: A multi-level basis in different spline spaces that preconditions the linear system arising from a Galerkin discretization method of an elliptic boundary value problem of order \(2r\) is presented. In the well-organized paper they start to propose the problem and summarize the most general results of \textit{W. Dahmen} and \textit{A. Kunoth} [Numer. Math. 63, No. 3, 315-344 (1992; Zbl 0757.65031)] regarding the condition number. Section 2 gives their own result that the condition number is \(\kappa={\mathcal O}((n+1)^2)\) for the different spline spaces considered. In Section 3 the proofs are presented where the proof of theorem 5 gives a detailed description how to construct the locally supported basis. Only for one point, how to choose a minimal determining set of coefficients, they refer to earlier publications.
reviewed by: N.Herrmann
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 910305
zbMATH Keywords: finite element method
zbMATH Keywords: preconditioning
zbMATH Keywords: Galerkin method
zbMATH Keywords: multi-level basis
zbMATH Keywords: condition number
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00214-6
OpenAlex ID: W2073570719
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description: scientific article; zbMATH DE number 910305