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A Posteriori Error Control for Finite Element Approximations of the Integral Equation for Thin Wire Antennas
Author(s) -
Carstensen C.,
Rynne B.P.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200204)82:4<284::aid-zamm284>3.0.co;2-5
Subject(s) - finite element method , polygon mesh , a priori and a posteriori , mathematics , convergence (economics) , integral equation , harmonic , electromagnetic field , reliability (semiconductor) , partial differential equation , mathematical analysis , mathematical optimization , geometry , acoustics , physics , structural engineering , engineering , philosophy , power (physics) , epistemology , quantum mechanics , economics , economic growth
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.