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.
2010
BIT
50
377
394
Integrali parte finita; Integrali a valor principale di Cauchy; metodo agli elementi finiti spline; spline bivariate
Chong-Jun Li; Vittoria Demichelis; Catterina Dagnino
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/71029
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