Dimension and basis construction for C2-smooth isogeometric spline spaces over bilinear-like G2 two-patch parameterizations

We investigate the space of C2-smooth isogeometric functions over this specific class of two-patch geometries. The study is based on the equivalence of the C2-smoothness of an isogeometric function and the G2-smoothness of its graph surface (cf. Groisser and Peters (2015) and Kapl et al. (2015). The dimension of the space is computed and an explicit basis construction is presented. The resulting basis functions possess simple closed form representations, have small local supports, and are well-conditioned. In addition, we introduce a subspace whose basis functions can be generated uniformly for all possible configurations of bilinear-like G2 two-patch parameterizations. Numerical results obtained by performing L2-approximation and solving Poisson's equation indicate that already the subspace possesses optimal approximation properties.