Accuracy Analysis of Interpolating Element-Free Galerkin (IEFG) Method in Solving Transient Heat Conduction Problems

Abstract

For the interpolating element-free Galerkin (IEFG) method set up by combining the shape function constructed with interpolating moving least-squares (IMLS) approximation and Galerkin integral weak form of partial differential equation, we show that the task of accuracy analysis of the IEFG method in solving transient heat conduction problems can be reduced to the estimation of errors in the procedure of IMLS approximation and the integral weak form of heat conduction equation. Following this practice, accuracy analysis of IEFG method is derived. To illustrate our results, numerical tests are discussed by two examples and give an optimal convergence rate with respect to two types of norm.