The flow of a falling liquid film on an oscillating inclined plane is simulated numerically with Galerkin finite element method. The effects of oscillating frequency and initial perturbation frequency are investigated. A low-frequency modulation signal is observed in the flow field. Nonlinear effect of the low-frequency signal in the flow field promotes the coalescence of waves on a free surface, and accelerates the development of the waves. For higher oscillating frequencies, this effect is more apparent. A solitary hump is observed in the flow.

A Lagrangian finite element method is ued to simulate a uniformly heated film flowing down an inclined plate. An example with periodic inlet disturbances of different frequencies is computed,and the agreement with the linear stability theory shows that the Lagrangian finite element method has good resolution.The film flow is fully developed to saturated periodic wave,quasiperiodic wave,multipeaked wave and solitary hump.