Some refined Finite volume methods for elliptic problems with corner singularities

@inproceedings{Djadel2003SomeRF,
  title={Some refined Finite volume methods for elliptic problems with corner singularities},
  author={Karim Djadel and Serge Nicaise and Jalel Tabka},
  year={2003}
}
It is well known that the solution of the Laplace equation in a non convex polygonal domain of R has a singular behaviour near non convex corners. Consequently we investigate three re ned nite volume methods (cell-center, conforming nite volume-element and non conforming nite volume-element) to approximate the solution of such a problem and restore optimal orders of convergence as for smooth solutions. Numerical tests are presented and con rm the theoretical rates of convergence. 

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