Cs-smooth isogeometric spline spaces over planar bilinear multi-patch parameterizations.

The design of globally Cs-smooth (s ≥ 1) isogeometric spline spaces over multi-patch geometries with possibly extraordinary vertices, i.e. vertices with valencies different from four, is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods Kapl et al. Comput. Aided Geom. Des. 52–53:75–89, 2017, Kapl et al. Comput. Aided Geom. Des. 69:55–75, 2019 and Kapl and Vitrih J. Comput. Appl. Math. 335:289–311, 2018, Kapl and Vitrih J. Comput. Appl. Math. 358:385–404, 2019 and Kapl and Vitrih Comput. Methods Appl. Mech. Engrg. 360:112684, 2020 for the construction of C1-smooth and C2-smooth isogeometric spline spaces over particular planar multi-patch geometries to the case of Cs-smooth isogeometric multi-patch spline spaces of degree p, inner regularity r and of a smoothness s ≥ 1, with p ≥ 2s + 1 and s ≤ r ≤ p − s − 1. More precisely, we study for s ≥ 1 the space of Cs-smooth isogeometric spline functions defined on planar, bilinearly parameterized multi-patch domains, and generate a particular Cs-smooth subspace of the entire Cs-smooth isogeometric multi-patch spline space. We further present the construction of a basis for this Cs-smooth subspace, which consists of simple and locally supported functions. Moreover, we use the Cs-smooth spline functions to perform L2 approximation on bilinearly parameterized multi-patch domains, where the obtained numerical results indicate an optimal approximation power of the constructed Cs-smooth subspace. [ABSTRACT FROM AUTHOR]