Abstract: In order to eliminate the numerical oscillation caused by convection dominant of convection diffusion equation, the equation is transformed into its characteristics form firstly, and then the element free Galerkin method is proposed by using the moving least square basis functions. The convergence analysis of our method is analyzed, and two kinds of error analysis about the radius of the influence domain and time step are derived, respectively. The numerical examples are presented to discuss the comparison the new method with the finite element method as well. The numerical results show that the new method can be used to eliminate the numerical oscillation with a good convergence. Moreover, the accuracy of the new method is better than the finite element method by choosing the optimal penalty factor and dimensionless size. The new method is an effective numerical method for solving the convection-dominant diffusion equations.

Key words: convection diffusion equations, element free Galerkin method, moving least square basis function, error analysis