Local and adaptive refinement with hierarchical B-splines

Adaptive spline models for geometric modeling and spline-based PDEs solvers have recently attracted increasing attention both in the context of computer aided geometric design and isogeometric analysis. In particular, approximation spaces defined over extensions of tensor-product meshes which allow axis aligned segments with T-junctions are currently receiving particular attention. In this short paper we review some recent results concerning the characterization of the space spanned by the hierarchical B-spline basis. In addition, we formulate a refinement algorithm which allows us to satisfy the conditions needed for this characterization.