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We apply the hp-version of the boundary element method (BEM) for thenumerical solution of the electric field integral equation (EFIE) on aLipschitz polyhedral surface G. The underlying meshes are supposed to bequasi-uniform triangulations of G, and the approximations are based on eitherRaviart-Thomas or Brezzi-Douglas-Marini families of surface elements.Non-smoothness of G leads to singularities in the solution of the EFIE,severely affecting convergence rates of the BEM. However, the singularbehaviour of the solution can be explicitly specified using a finite set ofpower functions (vertex-, edge-, and vertex-edge singularities). In this paperwe use this fact to perform an a priori error analysis of the hp-BEM onquasi-uniform meshes. We prove precise error estimates in terms of thepolynomial degree p, the mesh size h, and the singularity exponents.

Natural hp-BEM for the electric field integral equation with singular solutions