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 C¹ hp-basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C¹ approach also includes varying polynomial degrees. The properties of the hp-basis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the C^k hp-basis functions based on B-splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.