Element-free Galerkin method to the interface problems with application in electrostatic

The purpose of this paper is to develop the element-free Galerkin method for a numerical simulation of the second-order elliptic equation with discontinuous coefficients. Discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. The proposed method is one of the powerful meshless methods based on moving least squares approximation. The element-free Galerkin method uses only a set of nodal points to discretize the governing equation. No mesh in the classical sense is needed, but a background mesh is used for integration purpose. A quadrilateral mesh unfitted with the interface is used for integration objective. The Lagrange multipliers are used to enforce both Dirichlet boundary condition and Dirichlet jump condition. The presented numerical experiments confirm the efficiency of the proposed method in comparison with some existing methods for interface problems. Copyright (c) 2016 John Wiley & Sons, Ltd.