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Curved Finite Element Methods for the Solution of Integral Singular Equations on Surfaces in R3

  • J. C. Nedelec
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 134)

Abstract

In NEDELEC-PLANCHARD [N.P.], we have shown that the singular integral equation on a closed surface Γ of R3:
$$\frac{1}{{4\pi }}\int\limits_\Gamma {\frac{{q(x)}}{{|x - y|}}} dx = u(y);y \in \Gamma $$
(1)
admits an unique solution, and is variational and coercive in the Hilbert space H−1/2(Γ).

In this paper, with the help of curved finite elements, we introduce an approximate surface Γh and an approximate problem on Γh , which solution is qh . Then, we study the error of approximation in some Hilbert spaces, between q , solution of (0), and qh , and also, between the two corresponding potentials u and uh .

Keywords

Hilbert Space Finite Element Method Integral Singular Equation Boundary Integral Equation Closed Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • J. C. Nedelec
    • 1
  1. 1.Centre de Mathématiques AppliquéesEcole PolytechniquePalaiseauFrance

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