A note on the meshless method using radial basis functions

In this paper, we prove some inverse inequalities for the finite dimensional subspace interpolated by radial basis functions. The properties of these inequalities are worse than those in finite element spaces. These bad properties result in a huge condition number for both the collocation method and Galerkin method using radial basis functions. As applications, theoretical estimates of the condition numbers of a meshless method using radial basis functions are given.