On very accurate enclosure of the optimal constant in the a priori error estimates for H20-projection

We present constructive a priori error estimates forH 0 -projection into a space of polynomials on a one-dimensional interval. Here, “constructive” indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants to be as small as possible. Using the proposed technique, the optimal constant could be enclosed in a very narrow interval with results verification. Furthermore, constructive error estimates for finite element H 0 projection in one dimension are presented. This type of estimates will play an important role in the numerical verification of solutions for nonlinear fourthorder elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method.