Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 89, 2012 - Issue 12
Submit an article Journal homepage
179
Views
7
CrossRef citations to date
0
Altmetric
Section B

Generalized Gaussian quadrature rules over regions with parabolic edges

K. V. Nagaraja Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore, IndiaCorrespondence[email protected]
&
Sarada Jayan Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore, India
Pages 1631-1640 | Received 01 Nov 2011, Accepted 23 Apr 2012, Published online: 25 May 2012

References

  • Asghar Bhatti , M. 2005 . Fundamental Finite Element Applications with Mathematica and Matlab Computations , New York : John Wiley and Sons Inc .
  • Bathe , K. J. 1996 . Finite Element Procedures , Englewood Cliffs, NJ : Prentice-Hall .
  • Cowper , G. R. 1973 . Gaussian quadrature formulas for triangle . Int. J. Num. Meth. Eng. , 7 : 405 – 408 .
  • Hammer , P. C. and Stroud , A. H. 1956 . Numerical integration over simplexes . Math. Tables Other Aids Comput. , 10 : 137 – 139 .
  • Hammer , P. C. and Stroud , A. H. 1958 . Numerical evaluation of multiple integrals . Math. Tables Other Aids Comput. , 12 : 272 – 280 .
  • Hammer , P. C. , Marlowe , O. J. and Stroud , A. H. 1956 . Numerical integration over simplexes and coness . Math. Tables Other Aids Comput. , 10 : 130 – 136 .
  • Hillion , P. 1977 . Numerical integration on a triangle . Int. J. Num. Meth. Eng. , 11 : 797 – 815 .
  • Hughes , T. J.R. 1987 . “ The Finite Element Method, Static and Dynamic Analysis ” . Englewood Cliffs, NJ : Prentice-Hall .
  • Cavendish , J. C. , Gordon , W. J. and Hall , C. A. 1976 . Ritz Galerkin approximations in blending function spaces . Num. Math. , 26 : 155 – 178 .
  • Lague , G. and Baldur , R. 1977 . Extended numerical integration method for triangular surfaces . Int. J. Num. Meth. Eng. , 11 : 388 – 392 .
  • Lannoy , F. G. 1977 . Triangular finite elements and numerical integration . Comput. Struct. , 7 p. 613.
  • Laursen , M. E. and Gellert , M. 1978 . Some criteria for numerically integrated matrices and quadrature formulas for triangles . Int. J. Num. Meth. Eng. , 12 : 67 – 76 .
  • Lether , F. G. 1976 . Computation of double integrals over a triangle . J. Comput. Appl. Math. , 2 : 219 – 224 .
  • Ma , J. , Rokhlin , V. and Wandzura , S. 1996 . Generalized Gaussian quadrature rules for systems of arbitrary functions . SIAM J. Numer. Anal. , 33 ( 3 ) : 971 – 996 .
  • Rathod , H. T. , Nagaraja , K. V. , Venkatesudu , B. and Ramesh , N. L. 2004 . Gauss Legendre quadrature over a Triangle . J. Indian Inst. Sci. , 84 : 183 – 188 .
  • Rathod , H. T. , Shajedul and Karim , M. D. 2002 . An explicit integration scheme based on recursion for the curved triangular finite elements . Comput. Struct. , 80 : 43 – 76 .
  • Reddy , C. T. and Shippy , D. J. 1981 . Alternative integration formulae for triangular finite elements . Int. J. Num. Meth. Eng. , 17 : 133 – 139 .
  • McLeod , R. J.Y. and Murphy , R. 1979 . A numerical comparison of high order transformation and isoparametric transformation methods . Comput. Math. Appls. , 5 : 241 – 247 .
  • Sarada , J. and Nagaraja , K. V. 2011 . Generalized Gaussian quadrature rules over two-dimensional regions with linear edges . Appl. Math. Comput. , 217 : 5612 – 5621 .
  • Zienkiewicz , O. C. 1997 . “ The Finite Element Method ” . In , 3 , London : Mc Graw-Hill .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.