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

1 Citation (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
PublisherSpringer Verlag
Pages225-235
Number of pages11
Volume9553
ISBN (Print)9783319317687
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014 - Wurzburg, Germany
Duration: 2014 Sep 212014 Sep 26

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
Period14/9/2114/9/26

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)

Cite this

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).

Research output: Chapter in Book/Report/Conference proceedingConference 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)). 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. 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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