Abstract: The finite element solution of one dimensional stationary convection diffusion equation for waveproblems is summarized and analyzed. The reasons for wave are discussed and the basic principles and techniques which deal with the wave are also displayed. By using different interpolation functions, the results of finite element solutions are compared with that of the analytical solution. The wave and convergence of a finite elementsolution using an exponential function based interpolation (EFBI) are focally analyzed. The results show that the continuity improvement of interpolation functions can decrease the wave degree. Compared with the linerLagrange interpolation function, an EFBI function can simulate the distribution of variables within the unitaccurately and is effective to deal with the problem of numerical waves. In the condition of sparse grids, the finiteelement method using an EFBI function has a good solution.