A study on Sobolev orthogonal polynomials on a triangle

The main aim of this paper is to investigate Sobolev orthogonality and families of orthogonal polynomials on the triangle as a generalization of the results in Xu, Y. Constr. Approx. 46, 349-434 (2017). We define inner products or pseudo-inner products that contain derivatives up to third-order in the Sobolev space on a triangle and study associated orthogonal polynomials that are analogs of the Jacobi polynomials J(alpha,beta,gamma) (k,n) but with alpha,beta,gamma being -1, -2, or -3, and two other families derived under simultaneous permutations of (x,y,1-x-y) and (alpha,beta,gamma).