Numerical integration over polygons using an eight-node quadrilateral spline finite element

Authors:
Chong-Jun Li;Paola Lamberti;Catterina Dagnino
Affiliations:
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;Department of Mathematics, University of Torino, via C. Alberto, 10 Torino 10123, Italy;Department of Mathematics, University of Torino, via C. Alberto, 10 Torino 10123, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, a cubature formula over polygons is proposed and analysed. It is based on an eight-node quadrilateral spline finite element [C.-J. Li, R.-H. Wang, A new 8-node quadrilateral spline finite element, J. Comp. Appl. Math. 195 (2006) 54-65] and is exact for quadratic polynomials on arbitrary convex quadrangulations and for cubic polynomials on rectangular partitions. The convergence of sequences of the above cubatures is proved for continuous integrand functions and error bounds are derived. Some numerical examples are given, by comparisons with other known cubatures.