A finite element algorithm based on a modified characteristic-based split(CBS)scheme is proposed for the nonlinear fluid-membrane interactions at low Reynolds numbers.In this method,the flow field with moving boundaries is solved by an implicit scheme based on a combination of a modified semi-implicit CBS algorithm and the dual-time stepping method.The nonlinear vibration of the flexible membrane is computed by the Galerkin finite element method and the generalized-α method.The segment spring analogy method is applied for mesh moving.The fluid and structure solvers are coupled by the loosely-coupled partitioned method.Moreover,the Aitken-Δ2 method is introduced to accelerate the convergence process of the DTS at each time step.For verification,an example,namely a lid cavity with a flexible bottom,is presented to exam the stability and accuracy of the proposed fluid-structure interaction(FSI)method.An excellent agreement is obtained between the present results and the existing data from other papers and the proposed FSI method exhibits a good stability even when the computation is carried out to a very long time.Moreover,it is also found from the results that the computing speed of the DTS method can be increased about four times by the Aitken-Δ2 method.With little modification,this finite element solution procedure could be applied to other FSI problems with strong nonlinearity.