Convergence of the Natural $hp$-BEM for the Electric Field Integral Equation on Polyhedral Surfaces

  • Authors:
  • A. Bespalov;N. Heuer;R. Hiptmair

  • Affiliations:
  • albespalov@yahoo.com;nheuer@mat.puc.cl;hiptmair@sam.math.ethz.ch

  • Venue:
  • SIAM Journal on Numerical Analysis
  • Year:
  • 2010

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Abstract

We consider the variational formulation of the electric field integral equation on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on $\mathrm{div}_{\Gamma}$-conforming Raviart-Thomas boundary elements 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 degrees.