On Gauss-Lobatto Integration on the Triangle

Authors:
Yuan Xu
Affiliations:
yuan@math.uoregon.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

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Abstract

A recent result in [B. T. Helenbrook, SIAM J. Numer. Anal., 47 (2009), pp. 1304-1318] on the nonexistence 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.