Journal of Inequalities and Applications 2022(1) 2022年 [査読有り]
For the linear Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using the finite-element method (FEM). In solving the optimization ...
Xuefeng Liu Mitsuhiro T. Nakao Chun’guang You Shin’ichi Oishi
Japan Journal of Industrial and Applied Mathematics 38(2) 545-559 2021年6月 [査読有り]
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is solved by...
Journal of Computational and Applied Mathematics 371 2020年6月 [査読有り]
Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are further...
Japan Journal of Industrial and Applied Mathematics 36(2) 521-542 2019年7月 [査読有り]
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...
SIAM Journal on Numerical Analysis 57(3) 1395-1410 2019年 [査読有り]
To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed. Compared with the existing algorithm, which deals with e...
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