Numerical Verification of Solutions for Nonlinear Elliptic Problems Using anLResidual Method

Mitsuhiro T. Nakao, Nobito Yamamoto

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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
Volume217
Issue number1
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Numerical Verification of Solutions for Nonlinear Elliptic Problems Using anL<sup>∞</sup>Residual Method'. Together they form a unique fingerprint.

  • Cite this