A framework of verified eigenvalue bounds for self-adjoint differential operators

Xuefeng Liu*

*この研究の対応する著者

研究成果: Article査読

41 被引用数 (Scopus)

抄録

For eigenvalue problems of self-adjoint differential operators, a universal framework is proposed to give explicit lower and upper bounds for the eigenvalues. In the case of the Laplacian operator, by applying Crouzeix-Raviart finite elements, an efficient algorithm is developed to bound the eigenvalues for the Laplacian defined in 1D, 2D and 3D spaces. Moreover, for nonconvex domains, for which case there may exist singularities of eigenfunctions around re-entrant corners, the proposed algorithm can easily provide eigenvalue bounds. By further adopting the interval arithmetic, the explicit eigenvalue bounds from numerical computations can be mathematically correct.

本文言語English
ジャーナルApplied Mathematics and Computation
DOI
出版ステータスAccepted/In press - 2015

ASJC Scopus subject areas

  • 応用数学
  • 計算数学

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