Some remarks on the rigorous estimation of inverse linear elliptic operators

Takehiko Kinoshita; Yoshitaka Watanabe; Mitsuhiro T. Nakao

doi:10.1007/978-3-319-31769-4_18

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 proceeding › Conference 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 language	English
Title of host publication	Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers
Editors	Jürgen Wolff von Gudenberg, Warwick Tucker, Marco Nehmeier
Publisher	Springer Verlag
Pages	225-235
Number of pages	11
ISBN (Print)	9783319317687
DOIs	https://doi.org/10.1007/978-3-319-31769-4_18
Publication status	Published - 2016
Event	16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014 - Wurzburg, Germany Duration: Sept 21 2014 → Sept 26 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9553
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014
Country/Territory	Germany
City	Wurzburg
Period	9/21/14 → 9/26/14

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-31769-4_18

Cite this

Kinoshita, T., Watanabe, Y., & Nakao, M. T. (2016). Some remarks on the rigorous estimation of inverse linear elliptic operators. In J. W. von Gudenberg, W. Tucker, & M. Nehmeier (Eds.), Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers (pp. 225-235). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9553). Springer Verlag. https://doi.org/10.1007/978-3-319-31769-4_18

Some remarks on the rigorous estimation of inverse linear elliptic operators. / Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.
Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. ed. / Jürgen Wolff von Gudenberg; Warwick Tucker; Marco Nehmeier. Springer Verlag, 2016. p. 225-235 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9553).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kinoshita, T, Watanabe, Y & Nakao, MT 2016, Some remarks on the rigorous estimation of inverse linear elliptic operators. in JW von Gudenberg, W Tucker & M Nehmeier (eds), Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9553, Springer Verlag, pp. 225-235, 16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014, Wurzburg, Germany, 9/21/14. https://doi.org/10.1007/978-3-319-31769-4_18

Kinoshita T, Watanabe Y, Nakao MT. Some remarks on the rigorous estimation of inverse linear elliptic operators. In von Gudenberg JW, Tucker W, Nehmeier M, editors, Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. Springer Verlag. 2016. p. 225-235. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-31769-4_18

Kinoshita, Takehiko ; Watanabe, Yoshitaka ; Nakao, Mitsuhiro T. / Some remarks on the rigorous estimation of inverse linear elliptic operators. Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. editor / Jürgen Wolff von Gudenberg ; Warwick Tucker ; Marco Nehmeier. Springer Verlag, 2016. pp. 225-235 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Some remarks on the rigorous estimation of inverse linear elliptic operators

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