Smooth interpolation in triangles

Abstract

AbstractThe purpose of this paper is to describe new schemes of interpolation to the boundary values of a function defined on a triangle. These schemes are affine-invariant and combine several Hermite interpolants. They are not, however, finite dimensional schemes. The simplest scheme is exact for quadratic functions, uses rational linear weighting (“blending”) functions analogous to the methods of Mangeron and Coons for rectangles, and satisfies a maximum principle. For any positive integer p, there is an analogous scheme which interpolates on the boundary to the function and all its partial derivatives of order p − 1. The interpolant satisfies a partial differential equation of order 6p and approximates any sufficiently smooth function to order O(h3p)