Jackson-type inequalities for h-p clouds and error estimates

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 paper we prove Jackson-type inequalities for h-p cloud functions. These inequalities 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.