C^s-smooth isogeometric spline spaces over planar multi-patch parameterizations
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The design of globally C^s-smooth (s ≥ 1) isogeometric spline spaces over multi-patch geometries is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods [25,28] and [31-33] for the construction of C^1-smooth and C^2-smooth isogeometric spline spaces over particular planar multi-patch geometries to the case of C^s-smooth isogeometric multi-patch spline spaces of an arbitrary selected smoothness s ≥ 1. More precisely, for any s ≥ 1, we study the space of C^s-smooth isogeometric spline functions defined on planar, bilinearly parameterized multi-patch domains, and generate a particular C^s-smooth subspace of the entire C^s-smooth isogeometric multi-patch spline space. We further present the construction of a basis for this C^s-smooth subspace, which consists of simple and locally supported functions. Moreover, we use the C^s-smooth spline functions to perform L^2 approximation on bilinearly parameterized multi-patch domains, where the obtained numerical results indicate an optimal approximation power of the constructed C^s-smooth subspace.
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