An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

Abstract

This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.

Original languageEnglish
Pages (from-to)407-420
Number of pages14
JournalJapan Journal of Industrial and Applied Mathematics
Volume36
Issue number2
DOIs
Publication statusPublished - Jul 1 2019

Fingerprint

Dual space
Elliptic Operator
Linear Operator
A Priori Error Estimates
Invertibility
Projection
Norm

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

Cite this

An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space. / Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 36, No. 2, 01.07.2019, p. 407-420.

Research output: Contribution to journalArticle

@article{ffdfcb759ff24984a00e5be4fcaf727c,
title = "An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space",
abstract = "This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.",
author = "Yoshitaka Watanabe and Takehiko Kinoshita and Nakao, {Mitsuhiro T.}",
year = "2019",
month = "7",
day = "1",
doi = "10.1007/s13160-019-00344-8",
language = "English",
volume = "36",
pages = "407--420",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "2",

}

TY - JOUR

T1 - An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

AU - Watanabe, Yoshitaka

AU - Kinoshita, Takehiko

AU - Nakao, Mitsuhiro T.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.

AB - This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported.

UR - http://www.scopus.com/inward/record.url?scp=85061185049&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061185049&partnerID=8YFLogxK

U2 - 10.1007/s13160-019-00344-8

DO - 10.1007/s13160-019-00344-8

M3 - Article

VL - 36

SP - 407

EP - 420

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 2

ER -