Space of C2-smooth geometrically continuous isogeometric functions on planar multi-patch geometries: Dimension and numerical experiments

In particular, the dimension of this C2-smooth isogeometric space is investigated. The study is based on the decomposition of the space into three subspaces and is an extension of the work Kapl and Vitrih (2017) to the multi-patch case. In addition, we present an algorithm for the construction of a basis, and use the resulting globally C2-smooth functions for numerical experiments, such as performing L2 approximation and solving triharmonic equation, on bilinear multi-patch domains. The numerical results indicate optimal approximation order.