Jackson-type inequalities for h–p clouds and error estimates Original Research Article

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.