Estimation of the error of calculating the functional containing higher-order derivatives on a triangular grid

Abstract

In the present paper, it is proved that a functional containing second derivatives can be calculated with an error of order O(h 4m+1 ) with a triangular mesh of h → 0 if the piecewise polynomial functions of degree 4m + 1 for m ≥ 1. For n = 2 we give an example of the fact that the piecewise quadratic approximation gives the second order of accuracy for calculating the functional for a special kind of triangulation.