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Numerical integration over polygons using an eight-node quadrilateral spline finite element. (English) Zbl 1181.65043
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.

MSC:
65D32 Numerical quadrature and cubature formulas
65D07 Numerical computation using splines
41A55 Approximate quadratures
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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References:
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