A Symmetric Extended Gaussian Quadrature Formula for Evaluation of Triangular Domain Integrals

Farzana Hussain and M.S. Karim

This article proposed symmetrical Gaussian quadrature formulae for triangular domain integrals. As a result, it presents n×n points (for n>1) and points (for n>2) quadrature formulae in which the second one is totally free of crowding of Gaussian quadrature points and weights. By suitable transformation of a triangle in global space into its contiguous space, Gauss points and weights are computed which are symmetric about the line of symmetry. For clarity and reference, Gaussian integration points and weights for different values of n are presented in tabular form. The efficiency and accuracy of the schemes are tested through application examples. Finally, an error formula also presented to evaluate the error in monomial/polynomial integration using m×n points method successfully. The error calculated by the new error formula and the error in calculation of integrals by the proposed methods are found in good agreement.

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