A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation
type: Item
instance of: scholarly article
title: A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation
zbMATH Open document ID: 0595.65113
DOI: 10.1007/BF01408577
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133173
review text: The numerical solution of the linear equations arising from Morley's nonconforming displacement method is studied. In the first part of the paper a preconditioning is established by which the condition number is reduced to \(O(h^{-1})\). Specifically, two Poisson equations are solved with each iteration step. The second part is concerned with a multigrid algorithm. Due to the nonconformity of the elements some non-standard ingredients are necessary. In particular, a transfer step and a stepsize control is incorporated. Convergence is proved under the assumption of \(H^ 3\)-regularity. Numerical results are included.
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 3958645
zbMATH Keywords: biharmonic equation
zbMATH Keywords: nonconforming finite elements
zbMATH Keywords: preconditioned conjugate gradient methods
zbMATH Keywords: Morley's nonconforming displacement method
zbMATH Keywords: preconditioning
zbMATH Keywords: Poisson equations
zbMATH Keywords: multigrid algorithm
zbMATH Keywords: stepsize control
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
author: Petra Peisker
author: D. Braess
MaRDI profile type: Publication
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OpenAlex ID: W2063483315
description: scientific article; zbMATH DE number 3958645