Numerical verifications of solutions for nonlinear elliptic equations

Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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
Volume10
Issue number1
DOIs
Publication statusPublished - 1993 Feb
Externally publishedYes

Fingerprint

Nonlinear Elliptic Boundary Value Problem
Numerical Verification
Existence of Weak Solutions
Nonlinear Elliptic Equations
Finite Element Approximation
Numerical Techniques
Boundary value problems
Fixed point theorem
Error Estimates
Exact Solution
Verify
Numerical Examples
Operator

Keywords

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

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

Numerical verifications of solutions for nonlinear elliptic equations. / Watanabe, Yoshitaka; Nakao, Mitsuhiro T.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 10, No. 1, 02.1993, p. 165-178.

Research output: Contribution to journalArticle

Watanabe, Yoshitaka ; Nakao, Mitsuhiro T. / Numerical verifications of solutions for nonlinear elliptic equations. In: Japan Journal of Industrial and Applied Mathematics. 1993 ; Vol. 10, No. 1. pp. 165-178.
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