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Convergence of natural hp-BEM for the electric field integral equation on polyhedral surfaces

by A. Bespalov and N. Heuer and R. Hiptmair

(Report number 2009-24)

Abstract
We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on $Div_\Gamma$-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality of Galerkin solutions on sufficiently fine meshes or for sufficiently high polynomial degree.

Keywords: electromagnetic scattering, electric field integral equation (EFIE), Galerkin discretization, boundary element method (BEM), hp-refinement, non-coercive variational problems, smoothed Poincaré mapping, projection based interpolation

@Techreport{BHH09_36,
  author = {A. Bespalov and N. Heuer and R. Hiptmair},
  title = {Convergence of natural hp-BEM for the electric field integral equation on polyhedral surfaces},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-24},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-24.pdf },
  year = {2009}
}

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