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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.

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)
Full Text: DOI
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