Multivariate analysis-suitable T-splines of arbitrary degree

This paper defines analysis-suitable T-splines for arbitrary degree (including even and mixed degrees) and arbitrary dimension. We generalize the concept of anchor elements known from the two-dimensional setting, extend two existing concepts of analysis-suitability and justify their sufficiency for linear independence of the T-spline basis. Finally, we propose a local refinement scheme for multivariate T-splines that allows anisotropic refinement and preserves weak geometric analysis-suitability.