On C2 quintic spline functions over triangulations of Powell-Sabinʹs type

Given a triangulation Δ of a polygonal domain, we find a refinemet of Δ of Δ by choosing μt in a neighborhood of the center of the inscribed circle of each triangle of t ϵ Δ, connecting μt, to the vertices of the triangle t, and connecting μt to μt′ if t′ ϵ Δ shares an interior edge with t or to the midpoint νe of any boundary edge e of t. The resulting triangulation is a triangulation of Powell-Sabinʹs type. We investigate a C2 quintic spline space Š52(Δ) whose elements are C3 only at μtʹs. We give a dimension formula for this spline space, show how to construct a locally supported basis, display an interpolation scheme, and prove that this spline space has the full approximation order.