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We study the space of $C^{2}$-smooth isogeometric functions on bilinearlyparameterized multi-patch domains $\Omega \subset \mathbb{R}^{2}$, where thegraph of each isogeometric function is a multi-patch spline surface of bidegree$(d,d)$, $d \in \{5,6 \}$. The space is fully characterized by the equivalenceof the $C^2$-smoothness of an isogeometric function and the $G^2$-smoothness ofits graph surface, cf. (Groisser and Peters,2015; Kapl et al.,2015). This isthe reason to call its functions $C^{2}$-smooth geometrically continuousisogeometric functions. In particular, the dimension of this $C^{2}$-smoothisogeometric space is investigated. The study is based on the decomposition ofthe space into three subspaces and is an extension of the work (Kapl andVitrih, 2017) to the multi-patch case. In addition, we present an algorithm forthe construction of a basis, and use the resulting globally $C^{2}$-smoothfunctions for numerical experiments, such as performing $L^{2}$ approximationand solving triharmonic equation, on bilinear multi-patch domains. Thenumerical results indicate optimal approximation order.

Space of $C^2$-smooth geometrically continuous isogeometric functions on planar multi-patch geometries: Dimension and numerical experiments