Numerical integration over polygons using an eight-node quadrilateral spline finite element (Q732132)

The problem considered in this paper is the numerical evaluation of \({I_{\Omega}(f)={\displaystyle \int_{\Omega} f(x,y)dxdy}}\), were \({f\in C(\Omega)}\) and \({\Omega}\) is a polygonal domain in \({R^{2}}\). The evaluation of \({I_{\Omega} (f)}\) is based on an eight-node quadrilateral spline finite element (see \({[5]}\)). The convergence of the above cubatures and error bounds are derived. Some numerical examples are given, by comparison with other known cubatures.