Piecewise Quadratic Approximations on Triangles

The problem of constructing a function 4,(x, y) of two variables on a triangle, such that ~(x, y) and its first derivatives take given values at the vertices, where ¢(x, y) is composed of quadratic pieces, is considered. Two methods of constructing piecewise quadratic approximations are described which have the property that, if they are applied on each triangle of a triangulation, then ~(x, y) and its first derivatives are continuous everywhere.