A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems

M. T. Nakao, K. Hashimoto, Y. Watanabe

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalComputing (Vienna/New York)
Volume75
Issue number1 SPEC. ISS.
DOIs
Publication statusPublished - 2005 Jul
Externally publishedYes

Fingerprint

Invertibility
Elliptic Operator
Linear Operator
Nonlinear Problem
Numerical methods
Numerical Methods
Verify
Nonlinear Elliptic Problems
A Priori Error Estimates
Simplify
Projection
Numerical Examples

Keywords

  • Finite element method
  • Numerical verification
  • Unique solvability of linear elliptic problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. / Nakao, M. T.; Hashimoto, K.; Watanabe, Y.

In: Computing (Vienna/New York), Vol. 75, No. 1 SPEC. ISS., 07.2005, p. 1-14.

Research output: Contribution to journalArticle

Nakao, M. T. ; Hashimoto, K. ; Watanabe, Y. / A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. In: Computing (Vienna/New York). 2005 ; Vol. 75, No. 1 SPEC. ISS. pp. 1-14.
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