Smooth macro-elements on Powell-Sabin-12 splits

Abstract

Macro-elements of smoothness C r C^r are constructed on Powell- Sabin- 12 12 splits of a triangle for all r ≥ 0 r \ge 0 . These new elements complement those recently constructed on Powell-Sabin- 6 6 splits and can be used to construct convenient superspline spaces with stable local bases and full approximation power that can be applied to the solution of boundary-value problems and for interpolation of Hermite data.