Gauss Legendre quadrature over a triangle

Journal of the Indian Institute of Science

Volumn 84, Issue 5, 2004, Pages 183-188

  Rathod, H T ^a   Nagaraja, K V ^b   Venkatesudu, B ^c   Ramesh, N L ^d  

^a BANGALORE UNIVERSITY   (India)

^b AMRITA SCHOOL OF ENGINEERING   (India)

^c OXFORD COLLEGE OF ENGINEERING   (India)

^d M S RAMAIAH INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Extended numerical integration; Finite element method; Gauss Legendre quadrature; Numerical integration; Standard 2 square; Triangular elements

Indexed keywords

BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; FUNCTIONS; INTEGRAL EQUATIONS; INTEGRATION; MATHEMATICAL TRANSFORMATIONS;

EXTENDED NUMERICAL INTEGRATION; FINITE-ELEMENT METHODS; GAUSS LEGENDRE QUADRATURE; NUMERICAL INTEGRATION; STANDARD 2-SQUARE; TRIANGULAR ELEMENTS;

NUMERICAL ANALYSIS;

EID: 20044363504     PISSN: 09704140     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. P. C. Hammer, O. J. Marlowe and A. H. Stroud, Numerical integration over simplexes and cones, Math. Tables Other Aids Computation, 10, 130-136 (1956).
2. P. C. Hammer and A. H. Stroud, Numerical integration over simplexes, Math. Tables Other Aids Computation, 10, 137-139 (1956).
3. P. C. Hammer and A. H. Stroud, Numerical evaluation of multiple integrals, Math. Tables Other Aids Computation, 12, 272-280 (1958).
4. G. R. Cowper, Gaussian quadrature formulas for triangles, Int. J. Num. Meth. Engng, 7, 405-408 (1973).
5. J. N. Lyness and D. Jespersen, Moderate degree symmetric quadrature rules for the triangle, J. Inst. Math. Applic., 15, 19-32 (1975).
6. F. G. Lannoy, Triangular finite elements and numerical integration, Computers Struct., 7, 613 (1977).
7. D. P. Laurie, Automatic numerical integration over a triangle, CSIR Spec. Rep. WISK 273, National Institute for Mathematical Sciences, Pretoria (1977).
8. M. E. Laursen and M. Gellert, Some criteria for numerically integrated matrices and quadrature formulas for triangles, Int. J. Num. Meth. Engng, 12, 67-76 (1978).
9. F. G. Lether, Computation of double integrals over a triangle, J. Comp. Applic. Math., 2, 219-224 (1976).
10. P. Hillion, Numerical integration on a triangle, Int. J. Num. Meth. Engng, 11, 797-815 (1977).
11. G. Lague and R. Baldur, Extended numerical integration method for triangular surfaces, Int. J. Num. Meth. Engng, 11, 388-392 (1977).
12. C. T. Reddy, Improved three point integration schemes for triangular finite elements, Int. J. Num. Meth. Engng, 12, 1890-1896 (1978).
13. C. T. Reddy and D. J. Shippy, Alternative integration formulae for triangular finite elements, Int. J. Num. Meth. Engng, 17, 133-139 (1981).
14. H. T. Rathod and M. S. Karim, An explicit integration scheme based on recursion for curved triangular finite elements, Computers Struct., 80, 43-76 (2002).
15. M. Abramowicz and I. A. Stegun (eds), Handbook of mathematical functions, Dover (1964).