A nodal basis for 𝐶¹ piecewise polynomials of degree 𝑛≥5

Abstract

A basis for the space of C 1 {C^1} piecewise polynomials in two variables of degree n ⩾ 5 n \geqslant 5 is constructed. The basis is parametrized by "nodal variables," namely, the values and derivatives of the basis functions at a discrete set of points.