Convergence of Galerkin method solutions of the integral equation for thin wire antennas

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13 Citations (Scopus)

Abstract

In this paper we consider the Pocklington integro-differential equation for the current induced on a straight, thin wire by an incident harmonic electromagnetic field. We show that this problem is well posed in suitable fractional order Sobolev spaces and obtain a coercive or Carding type inequality for the associated operator. Combining this coercive inequality with a standard abstract formulation of the Galerkin method we obtain rigorous convergence results for Galerkin type numerical solutions of Pocklington's equation, and we demonstrate that certain convergence rates hold for these methods. © J.C. Baltzer AG, Science Publishers.

Original languageEnglish
Pages (from-to)251-259
Number of pages9
JournalAdvances in Computational Mathematics
Volume12
Issue number2-3
DOIs
Publication statusPublished - 1 Feb 2000

Keywords

  • Convergence rates
  • Electromagnetic scattering
  • Galerkin methods

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