Spectral investigations of Nitsche's method

Incompatible discretization methods provide added flexibility in computation by allowing meshes to be unaligned with geometric features and easily accommodating non-interpolatory approximations. Such formulations that are based on Nitsche's approach to enforce surface constraints weakly, which shares features with stabilized methods, combine conceptual simplicity and computational efficiency with robust performance. The basic workings of the method are well understood, in terms of a bound on the parameter. However, its spectral behavior has not been explored in depth. Such investigations can shed light on properties of the operator that effect the solution of boundary-value problems. Furthermore, incompatible discretizations are rarely used for eigenvalue problems. The spectral investigations lead to practical procedures for solving eigenvalue problems that are formulated by Nitsche's approach, with bearing on explicit dynamics.