Quasi-Interpolation In A Space Of C-2 Sextic Splines Over Powell-Sabin Triangulations

In this work, we study quasi-interpolation in a space of sextic splines defined over Powell-Sabin triangulations. These spline functions are of class C-2 on the whole domain but fourth-order regularity is required at vertices and C-3 regularity is imposed across the edges of the refined triangulation and also at the interior point chosen to define the refinement. An algorithm is proposed to define the Powell-Sabin triangles with a small area and diameter needed to construct a normalized basis. Quasi-interpolation operators which reproduce sextic polynomials are constructed after deriving Marsden's identity from a more explicit version of the control polynomials introduced some years ago in the literature. Finally, some tests show the good performance of these operators.