Estimation of interpolation error constants for the triangular finite element

We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. We obtain explicit relotions for the dependence of such error constants on the geometric parameters of triangles. In particular, we explicitly determine the Babuska-Aziz constant, which plays an essential role in the interpolation error estimation of the linear triangular finite element The equation for determination is the transcendental equation √λ+tan √λ = 0, so that the solution can be numerically obtained with desired accuracy and verification. Such highly accurate approximate values for the constant as well as estimates for other constants can be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of finite element solutions. .