A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

    研究成果: Contribution to journalArticle査読

    10 被引用数 (Scopus)

    抄録

    This paper presents constructive a posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations (PDEs) on a bounded domain. This type of estimate plays an important role in the numerical verification of the solutions for boundary value problems in nonlinear elliptic PDEs. In general, it is not easy to obtain the a priori estimates of the operator norm for inverse elliptic operators. Even if we can obtain these estimates, they are often over estimated. Our proposed a posteriori estimates are based on finite-dimensional spectral norm estimates for the Galerkin approximation and expected to converge to the exact operator norm of inverse elliptic operators. This provides more accurate estimates, and more efficient verification results for the solutions of nonlinear problems.

    本文言語英語
    ページ(範囲)1543-1557
    ページ数15
    ジャーナルMathematics of Computation
    82
    283
    DOI
    出版ステータス出版済み - 2013

    All Science Journal Classification (ASJC) codes

    • 代数と数論
    • 計算数学
    • 応用数学

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