Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
type: Item
instance of: scholarly article
title: Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
zbMATH Open document ID: 0833.65131
published in: Applications of Mathematics
publication date: 1996-03-14T00:00:00Z
full work available at URL: https://eudml.org/doc/32917
review text: The mixed finite element discretization of second-order elliptic boundary value problems is considered. The efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations is studied. The authors present two multilevel solvers. The first one is based on ideas from the domain decomposition approach. A multilevel preconditioned conjugate gradient iteration acting on an appropriate subspace with a hierarchical type preconditioner that can be derived by subspace decomposition is presented. The second algorithm is obtained from the mixed hybridization and an alternative adaptive multilevel method based on this technique is derived. The local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be obtained by a defect correction in higher order ansatz spaces or by taking into account the superconvergence results. The performance of both algorithms is illustrated by two test examples. The solution of the first problem has a peak in an internal point while the solution of the second example has boundary layers.
reviewed by: Krassimir Georgiev
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 806349
zbMATH Keywords: mixed finite element
zbMATH Keywords: second-order elliptic boundary value problems
zbMATH Keywords: nonuniform triangulations
zbMATH Keywords: domain decomposition
zbMATH Keywords: multilevel preconditioned conjugate gradient iteration
zbMATH Keywords: adaptive multilevel method
zbMATH Keywords: local refinement
zbMATH Keywords: error estimators
zbMATH Keywords: defect correction
zbMATH Keywords: superconvergence
zbMATH Keywords: performance
zbMATH Keywords: test examples
zbMATH Keywords: boundary layers
author: R. H. W. Hoppe
author: B. Wohlmuth
describes a project that uses: PLTMG
MaRDI profile type: Publication
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OpenAlex ID: W12905223
DOI: 10.21136/AM.1995.134292
description: scientific article; zbMATH DE number 806349