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

摘要

We introduce the class of Phi-triangulations of a finite set P of points in R-n analogous to the classical Delaunay triangulation. Such triangulations can be constructed using the condition of empty intersection of P 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 R-n. We show how Phi-triangulations can be used to obtain error bounds for an approximation of the derivatives of C-2-smooth functions by piecewise linear functions.