Some improvements of invertibility verifications for second-order linear elliptic operators

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

Abstract

This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L2-norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported.

Original languageEnglish
Pages (from-to)36-46
Number of pages11
JournalApplied Numerical Mathematics
Volume154
DOIs
Publication statusPublished - Aug 2020

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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