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

C. Carstensen; B. P. Rynne

doi:10.1002/1521-4001(200204)82:4<284::AID-ZAMM284>3.0.CO;2-5

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

C. Carstensen, B. P. Rynne

Research output: Contribution to journal › Article

7 Citations (Scopus)

Abstract

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 experiments. © WILEY-VCH Verlag Berlin GmbH.

Original language	English
Pages (from-to)	284-288
Number of pages	5
Journal	Zeitschrift für Angewandte Mathematik und Mechanik
Volume	82
Issue number	4
DOIs	https://doi.org/10.1002/1521-4001(200204)82:4<284::AID-ZAMM284>3.0.CO;2-5
Publication status	Published - 2002

Keywords

A posteriori error estimate
Electromagnetic scattering
Finite element approximations
Thin wire antennas

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10.1002/1521-4001(200204)82:4<284::AID-ZAMM284>3.0.CO;2-5

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AB - 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 experiments. © WILEY-VCH Verlag Berlin GmbH.

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