A \(C^r\) trivariate macro-element based on the Worsey-Farin split of a tetrahedron
A superspline space on a special tetrahedral refinement of any arbitrary tetrahedral partition is considered. The tetrahedral refinement is called the Worsey-Farin refinement scheme and consist of splitting each tetrahedron of a partition into twelve subtetrahedra, which involves splitting each face with the well known bivariate Clough-Tocher split. The trivariate \(C^r\) macro-elements for any \(r\geq 1\) over the Worsey-Farin refinement of any tetrahedral partition are constructed. This extends the construction of \(C^1\) cubic Worsey-Farin elements and \(C^2\) elements of degree nine to the \(C^r\) situation with \(r>2\). It is shown that the degree of the polynomials used for proposed the macro-elements is the lowest.
scientific article; zbMATH DE number 6138629