A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines

Abstract

We introduce a simplex spline basis for a space of C 1 C^1 -quadratics on the well-known Powell-Sabin 12-split triangular region. Among its many important desirable properties, we show that it has an associated recurrence relation for evaluation and differentiation. Also developed are a Marsden-like identity, quasi-interpolants, approximation methods exhibiting unconditional stability, a subdivision scheme, and smoothness conditions across macro-element edges.