Spline‐ and hp ‐basis functions of higher differentiability in the finite cell method

In this paper, the use of hp ‐basis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, C k hp ‐basis functions based on classical B‐splines and a new approach for the construction of C 1 hp ‐basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C 1 approach also...