  We present a systematic study on higher-order penalty techniques for
isogeometric mortar methods. In addition to the weak-continuity enforced by a
mortar method, normal derivatives across the interface are penalized. The
considered applications are fourth order problems as well as eigenvalue
problems for second and fourth order equations. The hybrid coupling enables the
discretization of fourth order problems in a multi-patch setting as well as a
convenient implementation of natural boundary conditions. For second order
eigenvalue problems, the pollution of the discrete spectrum - typically
referred to as 'outliers' - can be avoided.
  Numerical results illustrate the good behaviour of the proposed method in
simple systematic studies as well as more complex multi-patch mapped geometries
for linear elasticity and Kirchhoff plates.
