Determination of the Babuska-Aziz Constant for the Linear Triangular Finite Element

Abstract

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 $t + \tan t = 0$, so that the solution can be numerically obtained with desired accuracy and verification. Such highly accurate approximate values for the constant can be widely used for a priori and a posteriori error estimations in adaptive computation and/or numerical verification.