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

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao

研究成果: ジャーナルへの寄稿記事

9 引用 (Scopus)

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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.

元の言語英語
ページ(範囲)1543-1557
ページ数15
ジャーナルMathematics of Computation
82
発行部数283
DOI
出版物ステータス出版済み - 5 30 2013

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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