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

We apply the hp -version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface G. The underlying meshes are supposed to be quasi-uniform triangulations of G, and the approximations are based on either Raviart-Thomas or Brezzi-Douglas-Marini families of surface elements. Nonsmoothness of G leads to singularities in the solution of the EFIE, severely affecting convergence rates of the BEM. However, the singular behavior of the solution can be explicitly specified using a finite set of functions (vertex-, edge-, and vertex-edge singularities), which are the products of power functions and poly-logarithmic terms. In this article, we use this fact to perform an a priori error analysis of the hp -BEM on quasi-uniform meshes. We prove precise error estimates in terms of the polynomial degree p, the mesh size h, and the singularity exponents. (c) 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012