Tetrahedral \(C^m\) interpolation by rational functions (Q2725278)

The authors use the rational form to construct a locally \(C^m\) interpolant for any integer \(m\geq 0\). They require \(C^{2m}\) data at the vertices and \(C^m\) data on the faces of a tetrahedron and use a polynomial of degree \(4m+1\) plus a rational term with denominator degree at most \(3m\). The scheme can have either \(4m+1\) order algebraic precision if \(C^{2m}\) data at the vertices and \(C^m\) data on the faces are given. Also, the resulting interpolant and its partial derivatives up to order \(m\) are polynomials on the boundaries of the tetrahedron.