Appropriate Gaussian quadrature formulae for triangles

International Journal of Applied Mathematics and Computation

M. S. Karim¹  Farzana Hussain²  Razwan Ahamad² 

[1] ProfessorDepartment of MathematicsShahjalal University of Science & TechnologySylhet -3114Bangladesh$$;Assistant ProfessorDepartment of MathematicsShahjalal University of Science & TechnologySylhet -3114Bangladesh$$

关键词: Extended Gaussian;    Triangular domain;    Numerical accuracy;    Convergence;   

DOI  :  10.0000/ijamc.2012.4.1.314

来源: PSIT Kanpur

【 摘 要 】

This paper mainly presents higher order Gaussian quadrature formulae for numerical integration over the triangular surfaces. In order to show the exactness and efficiency of such derived quadrature formulae, it also shows first the effective use of available gaussian quadrature for square domain integrals to evaluate the triangular domain integrals. Finally, it presents nxn points and n(n+1)/2 - 1 points (for n >1) Gaussian quadrature formulae for triangle utilizing n-point one-dimensional Gaussian quadrature. By use of simple but straightforward algorithms, gaussian points and corresponding weights are calculated and presented for clarity and reference. The proposed n(n+1)/2 - 1 points formulae completely avoids the crowding of gaussian points and overcomes all the drawbacks in view of accuracy and efficiency for the numerical evaluation of the triangular domain integrals of any arbitrary functions encountered in the realm of science and engineering.

【 授权许可】

Unknown