Comparison of implementation techniques for Galerkin projection between different meshes

To solve multiphysics problems, weak coupling of finite element calculations can be carried out: the subproblems of which the physical nature differs are solved separately on their own meshes. In this case, Galerkin projection provides useful tool to ensure the transfer of physical fields between different meshes. In terms of implementation, the Galerkin projection system can be either accurately assembled over the intersection of two meshes or approximately integrated over the target mesh. This paper describes and compares these two implementation techniques for the Galerkin projection