Some remarks on the rigorous estimation of inverse linear elliptic operators

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

研究成果: Conference contribution

2 引用 (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.

元の言語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
出版者Springer Verlag
ページ225-235
ページ数11
9553
ISBN(印刷物)9783319317687
DOI
出版物ステータスPublished - 2016
外部発表Yes
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 212014 9 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)
9553
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

Other

Other16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014
Germany
Wurzburg
期間14/9/2114/9/26

Fingerprint

Elliptic Operator
Partial differential equations
Linear Operator
Mathematical operators
Numerical methods
Mesh
Invertibility
Elliptic Partial Differential Equations
Approximation Property
Nonlinear Partial Differential Equations
Elliptic Problems
Estimate
Computational Cost
Costs
Numerical Methods
Subspace
Finite Element
Upper bound
Norm
Operator

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

これを引用

Kinoshita, T., Watanabe, Y., & Nakao, M. T. (2016). 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 (巻 9553, pp. 225-235). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 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. 巻 9553 Springer Verlag, 2016. p. 225-235 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻 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. : Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. 巻. 9553, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 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. : Scientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers. 巻 9553. Springer Verlag. 2016. p. 225-235. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/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. 巻 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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