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 fora fluid–solid interaction problem. The method, which combinesa standard finite element discretization in the fluid regionand 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 formulatedand analysed. Optimal order a priori error estimates in theenergy norm are shown. The main difficulty in the analysis iscaused by the two interface conditions which describe the interactionbetween the fluid and the solid. This is overcome by explicitlybuilding one of the interface conditions into the finite elementspaces. Iterative substructuring algorithms are also proposedfor effectively solving the discrete finite element equations.