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

摘要

In the present paper, it is proved that a functional containingsecond derivatives can be calculated with an error of order O(h4m+1)with a triangular mesh of h ! 0 if the piecewise polynomial functions ofdegree 4m+ 1 for m 1. For n = 2 we give an example of the fact thatthe piecewise quadratic approximation gives the second order of accuracyfor calculating the functional for a special kind of triangulation.