Correction of Gauss Legendre quadrature over a triangle

Abstract

Based on the remainder term for Gauss-Legendre quadrature rule, a correction formula for numerical integration over a triangle is proposed. The new formula increases the algebraic accuracy at least two-order in comparison with the original Gauss-Legendra quadrature rules, which were recently derived by Rathod et al. Results obtained with the correction formulae are compared with the existing formulae. It is shown that the correction formula has higher accuracy than the existing formulae. Thus it is of great use in many engineering applications.