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Control volume finite element method to solve incompressible flow problems was investigated. The streamline FCBI method was built and compared with the original FCBI and general FCBI method. Lid-driven cavity flow and S-channel flow were chosen as the test cases. The similarities and differences among the three interpolation functions were discussed according to the analysis. The results showed that for convection-dominated flow, especially with complex performances, the Streamline FCBI method could better describe the velocity distributions in the element and achieve more stable converged results. For convection-diffusion problems, the precision of all the methods were low when element Re was high. From the analysis that for convection-diffusion problems, it is concluded that good results can be achieved by using FCBI methods when element Re is less than 5.