A priori error estimates for a coupled finite element method and mixed finite element method for a fluid–solid interaction problem

This paper presents a heterogeneous finite element method for a fluid–solid interaction problem. The method, which combines a standard finite element discretization in the fluid region and a mixed finite element discretization in the solid region, allows the use of different meshes in fluid and solid regions. Both semi‐discrete and fully discrete approximations are formulated and analysed. Optimal order a priori error estimates in the energy norm are shown. The main difficulty in the analysis is caused by the two interface conditions which describe the interaction between the fluid and the solid. This is overcome by explicitly building one of the interface conditions into the finite element spaces. Iterative substructuring algorithms are also proposed for effectively solving the discrete finite element equations.