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-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. This research has been published in Mathematics of Computation. © 2013 American Mathematical Society