AbstractWe present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of ( with T-splines) and main differences when using in contrast to . The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on , T-splines may be applied to various different PDEs.