Optimal estimation for the Fujino–Morley interpolation error constants

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 t...

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Bibliographic Details
Published inJapan journal of industrial and applied mathematics Vol. 36; no. 2; pp. 521 - 542
Main Authors Liao, Shih-Kang, Shu, Yu-Chen, Liu, Xuefeng
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.07.2019
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Eigenvalues
Finite element method
Interpolation
Lower bounds
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
Perturbation
Quantitative analysis
Upper bounds
Finite element method
Fujino–Morley interpolation operator
35P15
97N50
Verified computing
Eigenvalue problem
65N30
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Summary: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/ .
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-019-00351-9