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

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

Research output: Contribution to journalArticle

28 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 - Jul 1 2005

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

All Science Journal Classification (ASJC) codes

  • 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, Yoshitaka.

In: Computing (Vienna/New York), Vol. 75, No. 1 SPEC. ISS., 01.07.2005, p. 1-14.

Research output: Contribution to journalArticle

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