Finite-part integrals over polygons by an 8-node quadrilateral spline finite element

@article{Li2010FinitepartIO,
  title={Finite-part integrals over polygons by an 8-node quadrilateral spline finite element},
  author={Chong-Jun Li and Vittoria Demichelis and Catterina Dagnino},
  journal={BIT Numerical Mathematics},
  year={2010},
  volume={50},
  pages={377-394}
}
In this paper we consider the numerical integration on a polygonal domain Ω in ℝ2 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… CONTINUE READING