Optimal estimation for the Fujino–Morley interpolation error constants

Shih Kang Liao, Yu Chen Shu, Xuefeng Liu

Research output: Contribution to journalArticle

Abstract

The quantitative estimation for the interpolation error constants of the Fujino–Morley interpolation operator is considered. To give concrete upper bounds for the constants, which is reduced to the problem of providing lower bounds for eigenvalues of bi-harmonic operators, a new algorithm based on the finite element method along with verified computation is proposed. In addition, the quantitative analysis for the variation of eigenvalues upon the perturbation of the shape of triangles is provided. Particularly, for triangles with longest edge length less than one, the optimal estimation for the constants is provided. An online demo with source codes of the constants calculation is available at http://www.xfliu.org/onlinelab/.

Original languageEnglish
Pages (from-to)521-542
Number of pages22
JournalJapan Journal of Industrial and Applied Mathematics
Volume36
Issue number2
DOIs
Publication statusPublished - 2019 Jul 1

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Interpolation Error
Optimal Estimation
Mathematical operators
Interpolation
Triangle
Concretes
Eigenvalue
Finite element method
Biharmonic
Operator
Quantitative Analysis
Chemical analysis
Finite Element Method
Interpolate
Lower bound
Upper bound
Perturbation

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

Cite this

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Optimal estimation for the Fujino–Morley interpolation error constants. / Liao, Shih Kang; Shu, Yu Chen; Liu, Xuefeng.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 36, No. 2, 01.07.2019, p. 521-542.

Research output: Contribution to journalArticle

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