Adaptive remeshing and \(h-p\) domain decomposition
type: Item
instance of: scholarly article
title: Adaptive remeshing and \(h-p\) domain decomposition
zbMATH Open document ID: 0782.65145
DOI: 10.1016/0045-7825(92)90027-H
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1993-10-17T00:00:00Z
review text: An appropriate combination of mesh refinement (\(h\)-version) and increase of the shape functions' polynomial degree (\(p\)-version) yield, for linear elliptic boundary value problems, an exponential rate of convergence in the energy norm even if the exact solution is singular. The present paper presents a method which uses an \(h\)-\(p\)-approximation for a domain decomposition with fully overlapping domains, allowing \(C^ 0\)- continuous approximation for geometrically incompatible mesh refinement to be obtained [cf. \textit{J. H. Bramble, R. E. Ewing, R. R. Parashkevov} and \textit{J. E. Pasciak}, SIAM J. Sci. Stat. Comput. 13, No. 1, 397-410 (1992; Zbl 0746.65084)]. The method is applied to a reaction-diffusion problem resulting from semiconductor process simulation. By means of numerical examples it is illustrated that the foregoing approach is well suited for problems with sharp interior layers or shock-like behaviour.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 78A55
zbMATH DE Number: 429033
zbMATH Keywords: adaptive remeshing
zbMATH Keywords: \(h\)-\(p\) domain decomposition
zbMATH Keywords: \(h\)-version
zbMATH Keywords: \(p\)- version
zbMATH Keywords: mesh refinement
zbMATH Keywords: exponential rate of convergence
zbMATH Keywords: reaction- diffusion problem
zbMATH Keywords: semiconductor process simulation
zbMATH Keywords: numerical examples
zbMATH Keywords: sharp interior layers
zbMATH Keywords: shock-like behaviour
author: Ernst Rank
describes a project that uses: PLTMG
MaRDI profile type: Publication
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full work available at URL: 0045-7825(92)90027-h
OpenAlex ID: W2019266401
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description: scientific article; zbMATH DE number 429033