TY - JOUR
T1 - Optimal estimation for the Fujino–Morley interpolation error constants
AU - Liao, Shih Kang
AU - Shu, Yu Chen
AU - Liu, Xuefeng
N1 - Publisher Copyright:
© 2019, The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - 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/.
AB - 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/.
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U2 - 10.1007/s13160-019-00351-9
DO - 10.1007/s13160-019-00351-9
M3 - Article
AN - SCOPUS:85064342820
SN - 0916-7005
VL - 36
SP - 521
EP - 542
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 2
ER -