Some remarks on the rigorous estimation of inverse linear elliptic operators

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    3 Citations (Scopus)

    Abstract

    This paper presents a new numerical method to obtain the rigorous upper bounds of inverse linear elliptic operators. The invertibility of a linearized operator and its norm estimates give important informations when analyzing the nonlinear elliptic partial differential equations (PDEs). The computational costs depend on the concerned elliptic problems as well as the approximation properties of used finite element subspaces, e.g., mesh size or so. We show the proposed new estimate is effective for an intermediate mesh size.

    Original languageEnglish
    Title of host publicationScientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers
    EditorsJürgen Wolff von Gudenberg, Warwick Tucker, Marco Nehmeier
    PublisherSpringer Verlag
    Pages225-235
    Number of pages11
    ISBN (Print)9783319317687
    DOIs
    Publication statusPublished - 2016
    Event16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014 - Wurzburg, Germany
    Duration: Sep 21 2014Sep 26 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9553
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014
    CountryGermany
    CityWurzburg
    Period9/21/149/26/14

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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