Jackson's Inequalities for h-p Clouds and Error Estimates

Abstract

The interest in meshfree methods for solving boundary-value problems
has grown rapidly in recent years. A meshless method that has
attracted much interest in the community of computational mechanics is
the h-p clouds method. For this kind of applications it is fundamental
to analyze the orders of approximation. In this this paper we prove a
Jackson type inequality for h-p cloud functions. This inequality set
up a general framework for the theoretical analysis of high order
error estimates of the h-p clouds method, with the same remarkable
features of Finite Element theory.