In this paper we consider the numerical integration on a polygonal domain $\Omega$ in $\mathbb{R}^2$ of a function $F(x,y)$ which is integrable except at a point $P_0=(x_0,y_0) \in\> \stackrel{\circ}{\Omega}$, where $F$ becomes infinite of order two. We approximate either the finite-part or the two-dimensional Cauchy principal value of the integral by using a spline finite element method combined with a subdivision technique also of adaptive type. We prove the convergence of the obtained sequence of cubatures. Finally, to illustrate the behaviour of the proposed method, we present some numerical examples.
Finite-part integrals over polygons by an 8-nodes quadrilateral spline finite element
DEMICHELIS, Vittoria;DAGNINO, Catterina
2010-01-01
Abstract
In this paper we consider the numerical integration on a polygonal domain $\Omega$ in $\mathbb{R}^2$ of a function $F(x,y)$ which is integrable except at a point $P_0=(x_0,y_0) \in\> \stackrel{\circ}{\Omega}$, where $F$ becomes infinite of order two. We approximate either the finite-part or the two-dimensional Cauchy principal value of the integral by using a spline finite element method combined with a subdivision technique also of adaptive type. We prove the convergence of the obtained sequence of cubatures. Finally, to illustrate the behaviour of the proposed method, we present some numerical examples.File | Dimensione | Formato | |
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Demichelis2.pdf
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