This contribution focuses on application of an interpolation procedure between two finite element (FE) meshes which preserves physical quantities of an interest. The approach of [8] based on the combination of a computationally cheap interpolation method together with constraints enforcing conservation of desired quantities, like e.g. total mass, kinetic energy or potential energy, is followed. The application of this procedure called as the interpolation with restrictions is shown together with a remeshing procedure in the numerical simulation of human vocal fold vibrations. During this simulation the typical scenario is the almost complete closure of the airflow channel, where a remeshing procedure needs to be applied combined with the interpolation of the numerical approximations of physical quantities on the new mesh. The FE approximation of this FSI problem with a prior unknown motion of elastic structure is presented and the advantages of the interpolation with restrictions are shown.