Some remarks on the behaviour of the finite element solution in nonsmooth domains

Mitsuhiro T. Nakao, Takehiko Kinoshita

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this work, we consider the behaviour of the residual error using a smooth finite element solution for elliptic problems on nonconvex and nonsmooth domains. It is proved that, against expectations, the residual error is unbounded and actually diverges to infinity as the mesh size goes to zero. A numerical example which illustrates this phenomenon will be presented for the Poisson equation on an L-shaped domain using a C1 Hermite element, and similar results will be shown for a C0 element with a posteriori smoothing.

Original languageEnglish
Pages (from-to)1310-1314
Number of pages5
JournalApplied Mathematics Letters
Volume21
Issue number12
DOIs
Publication statusPublished - 2008 Dec
Externally publishedYes

Fingerprint

Nonsmooth Domains
Finite Element Solution
Poisson equation
Diverge
Hermite
Poisson's equation
Elliptic Problems
Smoothing
Infinity
Mesh
Numerical Examples
Zero

Keywords

  • Nonsmooth domain
  • Poisson equation
  • Residual error

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Some remarks on the behaviour of the finite element solution in nonsmooth domains. / Nakao, Mitsuhiro T.; Kinoshita, Takehiko.

In: Applied Mathematics Letters, Vol. 21, No. 12, 12.2008, p. 1310-1314.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Kinoshita, Takehiko. / Some remarks on the behaviour of the finite element solution in nonsmooth domains. In: Applied Mathematics Letters. 2008 ; Vol. 21, No. 12. pp. 1310-1314.
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