Discretization by finite elements of a model parameter dependent problem

Douglas N. Arnold

Research output: Contribution to journalArticlepeer-review

124 Scopus citations


The discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness, which appears as a parameter in the problem, on the accuracy. It is shown that the approximation achieved by a standard finite element method degenerates for thin beams. In contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter. The most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by Gauss quadratures.

Original languageEnglish (US)
Pages (from-to)405-421
Number of pages17
JournalNumerische Mathematik
Issue number3
StatePublished - Oct 1981


  • Subject Classifications: AMS(MOS): 65N30, CR: 5.17


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