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Discrete Fredholm properties and convergence estimates for the electric field integral equation


Author: Snorre H. Christiansen
Journal: Math. Comp. 73 (2004), 143-167
MSC (2000): Primary 65N12, 65N38, 78M15
DOI: https://doi.org/10.1090/S0025-5718-03-01581-3
Published electronically: July 1, 2003
MathSciNet review: 2034114
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Abstract: The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies, using orthogonal splittings of the Galerkin space. At resonant frequencies we show that the spurious electric currents radiate only weakly in the exterior domain. This is achieved through the study of some finitely degenerated problems in terms of LBB Inf-Sup estimates and the use of discrete Helmholtz decompositions.


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Additional Information

Snorre H. Christiansen
Affiliation: Matematisk Institutt, P.B. 1053 Blindern, N-0316 Oslo, Norway
MR Author ID: 663397
Email: snorrec@math.uio.no

Received by editor(s): December 26, 2000
Received by editor(s) in revised form: April 10, 2002
Published electronically: July 1, 2003
Additional Notes: This work received financial support from Thales Airborne Systems
Article copyright: © Copyright 2003 American Mathematical Society