L2 error estimates of unsymmetric RBF collocation for second order elliptic boundary value problems

Abstract

The paper proves convergence of unsymmetric radial basis functions (RBFs) collocation for second order elliptic boundary value problems on the bounded domains. By using Schaback’s linear discretization theory, $L^2$ error is obtained based on the kernel-based trial spaces generated by the compactly supported radial basis functions. The present theory covers a wide range of kernel-based trial spaces including stationary and non-stationary approximation. The convergence rates depend on the regularity of the solution, the smoothness of the computing domain, and the approximation of scaled kernel-based spaces. Some numerical examples are added for illustration.