Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element

Nobito Yamamoto, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

The verifications of solutions to weakly nonlinear elliptic equations by the method described e.g. by Nakao (1988, 1989), etc. are sometimes hardly accomplished when the right-hand sides of the equations are very large. To overcome such difficulties, a residual iteration technique with approximate solution was introduced by Nakao (1993). In the present paper, we propose an a posteriori method for the residual iteration, and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element.

Original languageEnglish
Pages (from-to)271-279
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume60
Issue number1-2
DOIs
Publication statusPublished - 1995 Jun 20
Externally publishedYes

Keywords

  • Nonlinear elliptic problem
  • Numerical verification
  • Residual iteration

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

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