Abstract: The recently proposed reduced element method for adaptive finite element (FE) analysis has been successfully applied to a series of initial and boundary value problems, yet there is a lack of detailed and comprehensive comparative analysis with other similar adaptive FE methods. By taking the one-dimensional non-self-adjoint boundary value problem as the model problem, four similar adaptive FE algorithms for the one-dimensional problem are investigated with the maximum norm adopted to control errors. The comparative computation and analysis are carried out to identify the advantages and disadvantages of the four methods. The comparative analysis shows that as an adaptive FE analysis method, especially from the point of view of the local refinement capability, the reduced element method not only stands out for being simple and straightforward in theory and implementation, but also is superior to other methods in terms of reliability, versatility and efficiency.