Hierarchical bases of spline spaces with highest order smoothness over hierarchical T-subdivisions

The prospect of applying spline spaces over T-subdivisions to adaptive isogeometric analysis is an exciting one. One major issue with spline spaces over T-subdivisions is in providing proper bases (shape functions) for finite element analysis. In this paper, we propose a method for the construction of hierarchical bases of a spline space with highest order smoothness over a consistent hierarchical T-subdivision. Our method is induced by the surjection condition, and this set of basis functions is hierarchically adaptive. We also present a concrete set of non-negative hierarchical bases over a T-subdivision and apply them in adaptive finite element analysis.

► An edge-based method for constructing basis functions is presented.
► The method generates hierarchical bases that can be used for adaptive FEA.
► The dimension of this spline space is geometric independent.