Some High Degree Gauss Legendre Quadrature Formulas for Triangles (International Journal of Engineering and Computer Science, 2017)
This paper presents a numerical integration formula for the evaluation of ( )∬ ( )where ( ) and is any polygonal domain in . That is a closed domain withboundary composed of N oriented piecewise line segments ( ) with end points( ), ( ) and ( ) (( ). We join each of these line segments to a reference point( ) interior to the domain . This creates a coarse mesh of N triangles ( ) in andeach of these arbitrary triangles have three straight sides. These arbitrary triangles can be divided intoarbitrary triangles ( ,2,3,…. ). by using the triangular mesh generation schemedeveloped in this paper. We transform each = (say) into a standard 1-square and then into a 2-squarewhich can be integrated by using Gauss Legendre quadraure rules.We obtain enhanced accuracy bydivision of these arbitrary triangles into four arbitrary triangles (e=1,2,3,4) without refining the alreadygenerated triangular mesh.We first derive three different integration formulas for the integral∬ ( )where (( ) ) Then weestablish the necessary numerical integration formulas which use the well known Gauss Legendrequadrature rules. Proposed numerical integration formula is applied to integrals over triangular andpolygonal domains with complicated integrands.