With the improved moving least-squares (IMLS) approximation, an orthogonal function
system with a weight function is used as the basis function. The combination of the element-
free Galerkin (EFG) method and the IMLS approximation leads to the development of the
improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to
study the partial differential equations that control the heat flow in three-dimensional space.
With the IEFG technique, the Galerkin weak form is employed to develop the discretized …

In this study, the interpolating element-free Galerkin (IEFG) method for solving three-
dimensional (3D) transient heat conduction problem is presented. By using the improved
interpolating moving least-squares (IIMLS) method to form the shape function, and using the
weak form of 3D transient heat conduction problems to obtain the discretized equations, the
formulae of the IEFG method are obtained. The shape function of the IIMLS method satisfies
the property of Kronecker delta function, and then the IEFG method can apply essential …