Numerical Verification of Solutions for Nonlinear Elliptic Problems Using anLResidual Method

Mitsuhiro T. Nakao*, Nobito Yamamoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


We consider a numerical enclosure method with guaranteedLerror bounds for the solution of nonlinear elliptic problems of second order. By using an a posteriori error estimate for the approximate solution of the problem with a higher orderC0-finite element, it is shown that we can obtain the guaranteedLerror bounds with high accuracy. A particular emphasis is that our method needs no assumption of the existence of the solution of the original nonlinear equation, but it follows as the result of computation itself. A numerical example that confirms the effectiveness of the method is presented.

Original languageEnglish
Pages (from-to)246-262
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1998 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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