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Gauss Legendre quadrature over a triangle

Publication Type : Journal Article

Publisher : Journal of the Indian Institute of Science

Source : Journal of the Indian Institute of Science, Volume 84, Number 5, p.183-188 (2004)

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Keywords : Boundary value problems, Extended numerical integration, Finite element method, Finite-element methods, Functions, Gauss Legendre quadrature, Integral equations, integration, Mathematical transformations, Numerical Analysis, Numerical integration, Standard 2-square, Triangular elements

Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Year : 2004

Abstract : This paper presents a Gauss Legendre quadrature method for numerical integration over the standard triangular surface: {(x, y) | 0 ≤ x, y ≤ 1, x + y ≤ 1} in the Cartesian two-dimensional (x, y) space. Mathematical transformation from (x, y) space to (ξ, η) space map the standard triangle in (x, y) space to a standard 2-square in (ξ, η) space: {(ξ, η)|-l ≤ ξ, η ≤ 1}. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points and yields results which are accurate and reliable. Results obtained with new formulae are compared with the existing formulae.

Cite this Research Publication : H. Ta Rathod, Dr. K.V. Nagaraja, Venkatesudu, Bc, and Ramesh, N. Ld, “Gauss Legendre quadrature over a triangle”, Journal of the Indian Institute of Science, vol. 84, pp. 183-188, 2004.

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