On Gauss-Lobatto integration on the triangle

TL;DR

This paper investigates the existence and construction of Gauss-Lobatto cubature rules on the triangle, establishing lower bounds on nodes and providing new construction methods and examples.

Contribution

It strengthens previous non-existence results by providing lower bounds and introduces a novel method for constructing Lobatto type cubature rules on the triangle.

Findings

Established a lower bound for nodes in Gauss-Lobatto rules on the triangle.

Developed a new construction method for Lobatto cubature rules.

Constructed several explicit examples of such rules.

Abstract

A recent result in [2] on the non-existence of Gauss-Lobatto cubature rules on the triangle is strengthened by establishing a lower bound for the number of nodes of such rules. A method of constructing Lobatto type cubature rules on the triangle is given and used to construct several examples.