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)


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
Issue number12
Publication statusPublished - 2008 Dec
Externally publishedYes



  • Nonsmooth domain
  • Poisson equation
  • Residual error

ASJC Scopus subject areas

  • Applied Mathematics

Cite this