A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

This paper presents constructive a posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations (PDEs) on a bounded domain. This type of estimate plays an important role in the numerical verification of the solutions for boundary value problems in nonlinear elliptic PDEs. In general, it is not easy to obtain the a priori estimates of the operator norm for inverse elliptic operators. Even if we can obtain these estimates, they are often over estimated. Our proposed a posteriori estimates are based on finite-dimensional spectral norm estimates for the Galerkin approximation and expected to converge to the exact operator norm of inverse elliptic operators. This provides more accurate estimates, and more efficient verification results for the solutions of nonlinear problems.

Original languageEnglish
Pages (from-to)1543-1557
Number of pages15
JournalMathematics of Computation
Volume82
Issue number283
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Constructive a posteriori estimates
  • Galerkin method
  • Linear elliptic PDEs

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Computational Mathematics

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