Quasi-Interpolation in a Space of C2 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 class C2 on the whole domain but fourth-order regularity is required at vertices and C3 imposed across edges refined triangulation also interior point chosen to define refinement. An algorithm proposed triangles with small area diameter needed construct normalized basis. Quasi-interpolation operators which reproduce polynomials constructed after deriving Marsden’s identity from more explicit version control introduced some years ago literature. Finally, tests show good performance these operators.