2019/03/30 by Shih-Kang Liao, Liao, Shih-Kang, Yu‐Chen Shu +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #35P15 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.1904.00186
openalex publication_date 2019/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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/.