C 1 Quadratic and C 2 Quartic Macro-Elements on a Modified Morgan-Scott Triangulation

In this paper, we construct a quadratic composite finite element of class C ¹ and quartic composite finite element of class C ² on a new triangulation τ ₁₀ which is obtained by splitting each triangle of a given triangulation τ into ten smaller subtriangles. These new elements can be used for constructing spline spaces with local basis that can be applied for solving some Hermite interpolation problems with optimal approximation order.