A decoupled finite element method for fluid–fluid interaction

A decoupled finite element method based on the scalar auxiliary variable and vector penalty projection approach is constructed and analysed for solving a fluid–fluid interaction problem, which includes two Navier–Stokes equations coupled by some nonlinear interface conditions. The proposed full-discrete scheme is a combination of mixed finite element approximation for spatial discretization, backward Euler scheme for temporal discretization, as well as explicit treatment for the interface conditions, and can penalize for lack of mass conservation. Furthermore, unconditional energy stability is given and error estimates for the fully discrete scheme are showed. Finally, some numerical experiments are provided to illustrate the theoretical results and efficiency of the presented method.