A multigrid method for a parameter dependent problem in solid mechanics
type: Item
instance of: scholarly article
title: A multigrid method for a parameter dependent problem in solid mechanics
zbMATH Open document ID: 0665.65077
DOI: 10.1007/BF01386441
author: C. Blömer
author: D. Braess
published in: Numerische Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133479
review text: In the finite element calculations of problems in solid mechanics the method of selected reduced integration (SRI) is frequently used to eliminate locking phenomena. Often SRI is equivalent to the application of a mixed method. When multigrid methods are applied the formulation as a mixed method is by far superior. This is shown by an analysis of the Timoshenko beam. It is proved that the convergence rate of the multigrid method for the mixed model is independent of the penalty parameter as the latter tends to zero. To this end a general theory for mixed methods with penalty terms is presented. The theoretical results are verified by numerical results for the mixed method and for the displacement model with SRI.
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4088871
zbMATH Keywords: finite element
zbMATH Keywords: method of selected reduced integration
zbMATH Keywords: locking
zbMATH Keywords: multigrid methods
zbMATH Keywords: Timoshenko beam
zbMATH Keywords: convergence rate
zbMATH Keywords: numerical results
reviewed by: D. Braess
MaRDI profile type: Publication
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OpenAlex ID: W2051828137
description: scientific article; zbMATH DE number 4088871