An approximate waves-bordering algorithm for adaptive finite elements analysis
type: Item
instance of: scholarly article
title: An approximate waves-bordering algorithm for adaptive finite elements analysis
zbMATH Open document ID: 0940.65029
DOI: 10.1023/A:1019101228064
published in: Numerical Algorithms
publication date: 2000-07-10T00:00:00Z
review text: The authors present a solution method for linear equations generated from a sequence of finite element meshes. The method assumes that each mesh in the sequence is largely the same as the previous mesh and that the changed portions are localized, as would be the case when a mesh is adaptively updated based on error estimates. The method is based loosely on work of \textit{C. Brezinski, M. Morandi Checchi} and \textit{M. Redivo-Zaglia} [SIAM J. Matrix Anal. Appl. 15, No. 3, 922-937 (1994; Zbl 0812.65017)] but is tailored for the case at hand. The solution method is briefly summarized in this paper, with details presented in a forthcoming companion paper. Unfortunately, the current paper does not contain sufficient detail to evaluate the method or its applicability. Neither are conditions described under which breakdown does not occur, nor are error estimates provided to establish the validity of the approximate waves-bordering algorithm. A numerical example is presented whose results indicate the potential of the algorithm when the number of mesh nodes is little changed from an earlier mesh.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1382969
zbMATH Keywords: approximate waves-bordering algorithm
zbMATH Keywords: direct solution methods
zbMATH Keywords: error estimates
zbMATH Keywords: finite element
zbMATH Keywords: numerical examples
author: M. Morandi Cecchi
author: F. Marcuzzi
reviewed by: Myron Sussman
MaRDI profile type: Publication
full work available at URL: a:1019101228064
OpenAlex ID: W22660658
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description: scientific article; zbMATH DE number 1382969