Stabilized IMLS based element free Galerkin method for stochastic elliptic partial differential equations

Abstract

In this paper, we propose a numerical method to solve the elliptic stochastic partial differential equations (SPDEs) obtained by Gaussian noises using an element free Galerkin method based on stabilized interpolating moving least square shape functions. The error estimates of the method is presented. The method is tested via several problems. The numerical results show the usefulness and accuracy of the new method.