  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/.
