Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles
ACM Transactions on Mathematical Software (TOMS)
Adaptive cubature over a collection of triangles using the d-transformation
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials
Computer Aided Geometric Design
Converting triangulations to quadrangulations
Computational Geometry: Theory and Applications
Experimental results on quadrangulations of sets of fixed points
Computer Aided Geometric Design
An encyclopaedia of cubature formulas
Journal of Complexity
An adaptive numerical cubature algorithm for simplices
ACM Transactions on Mathematical Software (TOMS)
A new 8-node quadrilateral spline finite element
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Numerical integration over polygons using an eight-node quadrilateral spline finite element
Journal of Computational and Applied Mathematics
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In this paper an adaptive numerical integration algorithm for polygons is constructed by cubatures based on finite quadrilateral elements, with particular reference to an 8-node spline finite element. Some numerical examples are given to evaluate the performance of the proposed algorithm, combined with several cubatures with accuracy of order two. The results are also compared with those obtained by two cubatures based on triangulation and a recent method based on the Green's integral formula and Gaussian rules.