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

Yoshitaka Watanabe*, Takehiko Kinoshita, Mitsuhiro T. Nakao

*この研究の対応する著者

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1543-1557
ページ数15
ジャーナルMathematics of Computation
82
283
DOI
出版ステータスPublished - 2013
外部発表はい

ASJC Scopus subject areas

  • 代数と数論
  • 応用数学
  • 計算数学

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