A new approach to apply the essential boundary conditions in element free Galerkin method for elliptic partial differential equations

The element free Galerkin method is a well-known method for solving partial differential equations. Applying essential boundary conditions in this method, that based on moving least squares approximation, have some complexities. Since the shape functions of the moving least squares approximation do not satisfy the property of Kronecker delta function, therefore imposing essential boundary conditions is not as trivial as in the finite element method and we need some modifications of the Galerkin weak form of the equation. In this paper we propose a new approach to apply essential boundary conditions in element free Galerkin method for solving elliptic PDEs. This approach is based on interpolating moving least square method. First we apply the essential boundary conditions in the moving least square approximation of the function then the approximation is used in element free Galerkin method. Thus the essential boundary condition is applied directly. In this paper we first introduce the interpolating moving least squares approximation, and then describe how to apply the boundary conditions. Finally, some different examples show the accuracy and efficiency of the method.