Approximation of the gradient of a function on the basis of a special class of triangulations

Abstract

We introduce the class of -triangulations of a finite set of points in analogous to the classical Delaunay triangulation. Such triangulations can be constructed using the condition of empty intersection of with the interior of every convex set in a given family of bounded convex sets the boundary of which contains the vertices of a simplex of the triangulation. In this case the classical Delaunay triangulation corresponds to the family of all balls in . We show how -triangulations can be used to obtain error bounds for an approximation of the derivatives of -smooth functions by piecewise linear functions.