Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems

Nitsche's method [11] is a classical method for imposing essential boundary conditions weakly. Unlike the penalty method, it is consistent with the original differential equation. The strong point of Nitsche's method is that it retains the convergence rate of the underlying finite element method, whereas the standard penalty method either requires a "very large" penalty parameter, destroying the condition number of the resulting matrix problem, or, in case the condition number is to be retained, is limited to first order energy-norm accuracy. In this paper, we give a formulation of Nitsche's method suitable for the problem of fluid-structure interaction. Numerical examples are given.