Error Analysis Of Interpolating Element-free Galerkin (IEFG) Method In Solving Transient Heat Conduction Problems

The main method used in this paper is interpolating element-free Galerkin(IEFG),one of the meshless methods.IEFG method is constructed by the combination of interpolating moving least squares(IMLS)approximation to get the shape function and Galerkin integral weak form to discretize the differential equations.Firstly,the IMLS approximation and its error estimates are discussed.Secondly,error 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,error analysis of IEFG method is derived.To illustrate the results,numerical tests are discussed through two examples and it turned out that two types of norm have the same convergence rate.Lastly,combining the shape function constructed by the IMLS method and Galerkin weak form for the generalized Fisher equations,IEFG method for the generalized Fisher equations is put forward,and the corresponding formulae are obtained.The boundary conditions can be directly applied in the IEFG method when solving partial differential equations.Numerical examples have verified that IEFG methodwill enhancecomputational efficiency.