Formula omitted] error estimates of unsymmetric RBF collocation for second order quasilinear elliptic equations

Abstract

The paper proves the convergence of unsymmetric radial basis functions collocation for second order quasilinear elliptic equations. L2 error is obtained based on the kernel-based trial spaces generated by the compactly supported radial basis functions. For the unsymmetric collocation case, we obtain the convergence result when the testing discretization is finer than the trial discretization. The convergence rates depend on the regularity of the solution, the Lipschitz continuity of the Frechét derivative of quasilinear operator, the smoothness of the computing domain, and the approximation of scaled kernel-based spaces.