On Sobolev orthogonal polynomials on a triangle

Abstract

We use the invariance of the triangle T2 = {(x, y) ∈ R2 : 0 < x, y, 1−x−y} under the permutations of {x, y, 1−x−y} to construct and study two-variable orthogonal polynomial systems with respect to several distinct Sobolev inner products defined on T2. These orthogonal polynomials can be constructed from two sequences of univariate orthogonal polynomials. In particular, one of the two univariate sequences of polynomials is orthogonal with respect to a Sobolev inner product and the other is a sequence of classical Jacobi polynomials.