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Numerische Mathematik

, Volume 88, Issue 1, pp 185–201 | Cite as

$C^1$ error estimation on the boundary for an exterior Neumann problem in $\mathbb R^3$

  • Arian Novruzi
Original article

Summary.

In this paper we establish a \(C^1\) error estimation on the boundary for the solution of an exterior Neumann problem in \(\mathbb R^3\). To solve this problem we consider an integral representation which depends from the solution of a boundary integral equation. We use a full piecewise linear discretisation which on one hand leads to a simple numerical algorithm but on the other hand the error analysis becomes more difficult due to the singularity of the integral kernel. We construct a particular approximation for the solution of the boundary integral equation, for the solution of the Neumann problem and its gradient on the boundary and estimate their \(C^0\) error.

Mathematics Subject Classification (1991): 65N38 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Arian Novruzi
    • 1
  1. 1.Université Henri Poincaré Nancy 1, Institut Elie Cartan, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France; e-mail: novruzi@iecn.u-nancy.fr FR

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