ABSTRACT
Abstract. Let Ω C H 2 be a rectangular domain subdivided into m n macrorectangles whose set of vertices is denoted by A . An additional set of m + n node lines divides each of them into four rectangles in which the diagonals are drawn. Let 52(Ω, Δ ) be the space of C l quadratic splines on the triangulation Δ obtained in this way and let S2 (Ω, Δ ) be the subspace of functions g £ 52(Ω, Δ ) whose gradient is linear on the edges of macrorectangles. We first construct a Hermite interpolant in this space whose data values are g ( A ) and D g ( A ) at all points A £ A . Then, by replacing partial derivatives by finite differences, we deduce a Lagrange interpolant on A . We give error bounds for C 3 functions and show the influence of node lines on the norm of the Lagrange projector.
