On Verified Computations of the Optimal Constant in the a Priori Error Estimates for H[sub 0][sup 2]-Projection
Mitsuhiro T. Nakao, Takehiko Kinoshita, Theodore E. Simos, George Psihoyios, Ch. Tsitouras · AIP conference proceedings · 2009
In this paper, we show some constructive a priori error estimates for H02‐projection into a space of polynomials on a one dimensional interval. Here, ’constructive’ means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H02‐projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.