A posteriori error control for finite element approximations of the integral equation for thin wire antennas

In this paper we discuss a finite element approximation method for solving the Pocklington integro-differential equation for the current induced on a straight, thin wire by an incident harmonic electromagnetic field. We obtain an a posteriori error estimate for finite element approximations of the equation, and we prove the reliability of this estimate. The theoretical results are then used to motivate an adaptive mesh-refining algorithm which generates very efficient meshes and yields optimal convergence rates in numerical ezperiments.

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