A robust nonconforming \(H^2\)-element
type: Item
instance of: scholarly article
zbMATH Open document ID: 0965.65127
DOI: 10.1090/S0025-5718-00-01230-8
author: Ragnar Winther
author: Trygve K. Nilssen
author: Xue-Cheng Tai
published in: Mathematics of Computation
publication date: 2001-02-19T00:00:00Z
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1566115
zbMATH Keywords: singular perturbation
zbMATH Keywords: nonconforming finite elements
zbMATH Keywords: uniform error estimates
zbMATH Keywords: uniform convergence
zbMATH Keywords: fourth-order elliptic equation
zbMATH Keywords: finite element methods
zbMATH Keywords: nonconforming Morley method
zbMATH Keywords: counterexample
MaRDI profile type: Publication
cites work: Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
cites work: Q4300595
cites work: Q4162607
cites work: Equivalence of Finite Element Methods for Problems in Elasticity
cites work: Q3470840
cites work: Q4082392
cites work: On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
cites work: Q4894342
title: A robust nonconforming \(H^2\)-element
review text: Finite element methods for some elliptic fourth-order singular perturbation problems are considered. It is shown that if such problems are discretized by the nonconforming Morley method, in a regime close to second-order elliptic equations, then the error increases. A counterexample is presented to show that the Morley method diverges for the reduced second-order equation.NEWLINENEWLINENEWLINEAn alternative to the Morley method is proposed to use a nonconforming \(H^2\)-element which is \(H^1\)-conforming. It is shown that the new finite element method converges in the energy norm uniformly in the perturbation parameter.
reviewed by: Zbigniew Dżygadło
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description: scientific article