Analysis and application of the interpolating element free Galerkin (IEFG) method to simulate the prevention of groundwater contamination with application in fluid flow

Abstract

We develop a meshless numerical procedure to simulate the groundwater equation (GWE). The used technique is based on the interpolating element free Galerkin (IEFG) method. The interpolating moving least squares (IMLS) approximation produces a set of functions such that they are well-known as “shape functions”. The IEFG technique employs the shape functions of IMLS approximation. The shape functions of IMLS approximation vanish on the boundary and also they satisfy the property of the Kronecker Delta function. Thus, Dirichlet boundary conditions can be exactly imposed. In this paper, we check the unconditional stability and convergence of the proposed numerical scheme based on the energy method. The numerical results confirm the theoretical analysis.