Asymmetric cubature formulas for polynomial integration in the triangle and square

Journal of Computational and Applied Mathematics

Volumn 218, Issue 1, 2008, Pages 184-191

  Taylor, Mark A ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Cubature; Fekete points; Multivariate integration; Polynomial approximation; Quadrature; Triangle

Indexed keywords

ALGORITHMS; FUNCTION EVALUATION; INTEGRATION; NUMERICAL METHODS;

ASYMMETRIC CUBATURE; FEKETE POINTS; MULTIVARIATE INTEGRATION;

POLYNOMIAL APPROXIMATION;

EID: 44449178746     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.04.050     Document Type: Article

References (14)

1. Cools R. Constructing Cubature Formulae: The Science Behind the Art, Acta Numerica vol. 6 (1997), Cambridge University Press, Cambridge, UK pp. 1-54
2. Cools R. Monomial cubature rules since Stroud: a compilation-part 2. J. Comput. Appl. Math. 112 (1999) 21-27
3. Cools R. An encyclopaedia of cubature formulas. J. Complexity 19 (2003) 445-453. http://www.cs.kuleuven.be/nines/ecf online database 〈http://www.cs.kuleuven.be/∼nines/ecf〉
4. Cools R., and Rabinowitz P. Monomial cubature rules since Stroud: a compilaton. J. Comput. Appl. Math. 48 (1993) 309-326
5. Dubiner M. Spectral methods on triangles and other domains. J. Sci. Comput. 6 (1991) 345-390
6. Koornwinder T. Two-variable analogues of the classical orthogonal polynomials. In: Askey R.A. (Ed). Theory and Applications of Special Functions (1975), Academic Press, New York 435-495
7. Lyness J., and Cools R. A survey of numerical cubature over triangles. Appl. Math. 48 (1994) 127-150
8. Lyness J., and Jespersen D. Moderate degree symmetric quadrature rules for the triangle. J. Inst. Math. Appl. 15 (1975) 19-32
9. Proriol J. Sur une famille de polynomes à deux variables orthogonaux dans un triangle. CR Acad. Sci. Paris 245 (1957) 2459-2461
10. Sherwin S., and Karniadakis G. A triangular spectral element method: applications to the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 123 (1995) 189-229
11. Solin P., Segeth K., and Dolezel I. Higher-Order Finite Element Methods (2004), Chapman & Hall/CRC Press, London, Boca Raton, FL
12. Taylor M.A., Wingate B.A., and Bos L.P. A cardinal function algorithm for computing multivariate quadrature points. SIAM J. Numer. Anal. 45 1 (2007) 193-205. http://link.aip.org/link/?SNA/45/193/1 URL 〈http://link.aip.org/link/?SNA/45/193/1〉
13. Taylor M.A., Wingate B.A., and Vincent R. An algorithm for computing Fekete points in the triangle. SIAM J. Numer. Anal. 38 (2000) 1707-1720
14. Wandzura S., and Xiao H. Symmetric quadrature rules on a triangle. Comput. Math. Appl. 45 (2003) 1829-1840