Numerical verifications of solutions for nonlinear elliptic equations

Yoshitaka Watanabe*, Mitsuhiro T. Nakao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.

Original languageEnglish
Pages (from-to)165-178
Number of pages14
JournalJapan Journal of Industrial and Applied Mathematics
Issue number1
Publication statusPublished - 1993 Feb
Externally publishedYes


  • finite element method
  • nonlinear boundary value problems
  • numerical verification

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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