Convergence of Galerkin method solutions of the integral equation for thin wire antennas
Author: Rynne, Bryan
Source: Advances in Computational Mathematics, Volume 12, Numbers 2-3, February 2000 , pp. 251-259(9)
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 Gårding 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.
Document Type: Research Article
Affiliations: Email: email@example.com
Publication date: February 2000