Some considerations of the invertibility verifications for linear elliptic operators

Mitsuhiro T. Nakao; Yoshitaka Watanabe; Takehiko Kinoshita; Takuma Kimura; Nobito Yamamoto

doi:10.1007/s13160-014-0160-6

Some considerations of the invertibility verifications for linear elliptic operators

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takehiko Kinoshita, Takuma Kimura, Nobito Yamamoto

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.

Original language	English
Pages (from-to)	19-31
Number of pages	13
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/s13160-014-0160-6
Publication status	Published - Mar 2015

All Science Journal Classification (ASJC) codes

Engineering(all)
Applied Mathematics

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10.1007/s13160-014-0160-6

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title = "Some considerations of the invertibility verifications for linear elliptic operators",

abstract = "This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.",

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AU - Kimura, Takuma

AU - Yamamoto, Nobito

N1 - Funding Information: The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 24340018, 23740074, and 24540151). Publisher Copyright: © 2015, The JJIAM Publishing Committee and Springer Japan.

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AB - This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.

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Some considerations of the invertibility verifications for linear elliptic operators

Abstract

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