A CrCr trivariate macro-element based on the Alfeld split of tetrahedra

We construct trivariate macro-elements of class CrCr for any r≥1r≥1 over the Alfeld refinement of any tetrahedral partition in R3R3. In our construction, the degree of polynomials used for these macro-elements is the lowest possible. We also give the dimension formula for the subspace of consisting of these macro-elements.