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

^*Corresponding author for this work

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 - 2015
Externally published	Yes

Keywords

Computer-assisted proof
Differential operators
Numerical verification
Solvability of linear problem

ASJC Scopus subject areas

Applied Mathematics
Engineering(all)

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10.1007/s13160-014-0160-6

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AU - Yamamoto, Nobito

PY - 2015

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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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KW - Differential operators

KW - Numerical verification

KW - Solvability of linear problem

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Some considerations of the invertibility verifications for linear elliptic operators

Abstract

Keywords

ASJC Scopus subject areas

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