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 language | English |
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Pages (from-to) | 251-259 |
Number of pages | 9 |
Journal | Advances in Computational Mathematics |
Volume | 12 |
Issue number | 2-3 |
DOIs | |
Publication status | Published - 1 Feb 2000 |
Keywords
- Convergence rates
- Electromagnetic scattering
- Galerkin methods