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IMA Journal of Numerical Analysis Advance Access published online on February 27, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn072
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Natural p-BEM for the electric field integral equation on screens

Alexei Bespalov{dagger}

Department of Mathematical Sciences, Brunel University, Uxbridge, West London UB8 3PH, UK

Norbert Heuer{ddagger}

Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile

{dagger} Email: albespalov{at}yahoo.com

{ddagger} Corresponding author. Email: nheuer{at}mat.puc.cl

Received on 18 February 2008. Revised on 15 September 2008.


  Abstract

In this paper we analyse the p-version of the boundary element method for the electric field integral equation on a plane open surface with polygonal boundary. We prove the convergence of the p-version with Raviart–Thomas parallelogram elements and derive an a priori error estimate that takes into account the strong singular behaviour of the solution at the edges and corners of the surface. The key ingredient of our analysis is the orthogonality of discrete Helmholtz decompositions in a Sobolev space of order Formula .

Key Words: p-version; electric field integral equation; time-harmonic electromagnetic scattering; boundary element method; singularities

Dedicated to Professor Martin Costabel on the occasion of his 60th birthday


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