Rational shape functions for \(C^ 1\)-interpolation on quadrilaterals (Q1352399)

The authors extend \textit{E. L. Wachspress}' construction [A rational finite element basis (1975; Zbl 0322.65001)] of a family of \(C^0\) splines on a quadrilateral grid to a family of \(C'\) splines. The spline functions are rational functions made up of linear factors. The existence proof from which a computational procedure can be extracted (it is not given explicitly) shows that there are still three constants that can be chosen subject to certain inequalities. The spline approximation is exact on functions of degree 3.