# American Institute of Mathematical Sciences

June  2015, 8(3): 619-647. doi: 10.3934/dcdss.2015.8.619

## Asymptotic boundary element methods for thin conducting sheets

 1 Research Center MATHEON, Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany 2 Seminar for Applied Mathematics, ETH Zurich, 8092 Zürich, Switzerland

Received  November 2013 Revised  June 2014 Published  October 2014

Various asymptotic models for thin conducting sheets in computational electromagnetics describe them as closed hyper-surfaces equipped with linear local transmission conditions for the traces of electric and magnetic fields. The transmission conditions turn out to be singularly perturbed with respect to limit values of parameters depending on sheet thickness and conductivity. We consider the reformulation of the resulting transmission problems into boundary integral equations (BIE) and their Galerkin discretization by means of low-order boundary elements. We establish stability of the BIE and provide a priori $h$-convergence estimates.
Citation: Kersten Schmidt, Ralf Hiptmair. Asymptotic boundary element methods for thin conducting sheets. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 619-647. doi: 10.3934/dcdss.2015.8.619
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