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

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

研究成果: ジャーナルへの寄稿記事

28 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)1-14
ページ数14
ジャーナルComputing (Vienna/New York)
75
発行部数1 SPEC. ISS.
DOI
出版物ステータス出版済み - 7 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

これを引用

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

:: Computing (Vienna/New York), 巻 75, 番号 1 SPEC. ISS., 01.07.2005, p. 1-14.

研究成果: ジャーナルへの寄稿記事

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