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

^*この研究の対応する著者

研究成果: Conference contribution

3 被引用数 (Scopus)

抄録

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.

本文言語	English
ホスト出版物のタイトル	Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers
出版社	Springer Verlag
ページ	225-235
ページ数	11
巻	9553
ISBN（印刷版）	9783319317687
DOI	https://doi.org/10.1007/978-3-319-31769-4_18
出版ステータス	Published - 2016
外部発表	はい
イベント	16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014 - Wurzburg, Germany 継続期間: 2014 9月 21 → 2014 9月 26

出版物シリーズ

名前	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
巻	9553
ISSN（印刷版）	0302-9743
ISSN（電子版）	1611-3349

Other

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

ASJC Scopus subject areas

理論的コンピュータサイエンス
コンピュータサイエンス（全般）

文献へのアクセス

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

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引用スタイル

Kinoshita, T., Watanabe, Y., & Nakao, M. T. (2016). Some remarks on the rigorous estimation of inverse linear elliptic operators. In Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers (Vol. 9553, 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. Vol. 9553 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).

研究成果: Conference contribution

Kinoshita, T, Watanabe, Y & Nakao, MT 2016, Some remarks on the rigorous estimation of inverse linear elliptic operators. in Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. vol. 9553, 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, 14/9/21. 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 Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. Vol. 9553. 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. Vol. 9553 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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