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We present a systematic study on higher-order penalty techniques forisogeometric mortar methods. In addition to the weak-continuity enforced by amortar method, normal derivatives across the interface are penalized. Theconsidered applications are fourth order problems as well as eigenvalueproblems for second and fourth order equations. The hybrid coupling enables thediscretization of fourth order problems in a multi-patch setting as well as aconvenient implementation of natural boundary conditions. For second ordereigenvalue problems, the pollution of the discrete spectrum - typicallyreferred to as 'outliers' - can be avoided.  Numerical results illustrate the good behaviour of the proposed method insimple systematic studies as well as more complex multi-patch mapped geometriesfor linear elasticity and Kirchhoff plates.

A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems