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

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)1543-1557
    Number of pages15
    JournalMathematics of Computation
    Volume82
    Issue number283
    DOIs
    Publication statusPublished - 2013

    All Science Journal Classification (ASJC) codes

    • Algebra and Number Theory
    • Computational Mathematics
    • Applied Mathematics

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