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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
$${I_{\Omega}(f)=\int_{\Omega} f(x,y)dxdy}$$, 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 $${}$$). 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)
##### Software:
Maple; Mathematica; Matlab
Full Text:
##### References:
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