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

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, which combines mortar and penalty methods, 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.