Isogeometric Analysis with Geometrically Continuous Functions on Planar Multi-Patch Geometries

We generate a basis of the space of bicubic and biquartic C-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω ⊂ R. The basis functions are obtained by suitably combining C-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [16]). They are described by simple explicit formulas for their spline coefficients. These C-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.