Space of C2-smooth geometrically continuous isogeometric functions on two-patch geometries

The space of C2-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is considered. The investigation of the dimension of the spaces of biquintic and bisixtic C2-smooth geometrically continuous isogeometric functions on such domains is presented. In addition, C2-smooth isogeometric functions are constructed to be used for performing L2-approximation and for solving triharmonic equation on different two-patch geometries. The numerical results indicate optimal approximation order.