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2010.88: Natural hp-BEM for the electric field integral equation with singular solutions

2010.88: Alexei Bespalov and Norbert Heuer (2010) Natural hp-BEM for the electric field integral equation with singular solutions.

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Abstract

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 $\Gamma$. 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. Non-smoothness of $\Gamma$ leads to singularities in the solution of the EFIE, severely affecting convergence rates of the BEM. However, the singular behaviour of the solution can be explicitly specified using a finite set of power functions (vertex-, edge-, and vertex-edge singularities). In this paper 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.

Item Type:MIMS Preprint
Uncontrolled Keywords:$hp$-version with quasi-uniform meshes, boundary element method, electric field integral equation, singularities, a priori error estimate
Subjects:MSC 2000 > 41 Approximations and expansions
MSC 2000 > 65 Numerical analysis
MSC 2000 > 78 Optics, electromagnetic theory
MIMS number:2010.88
Deposited By:Alex Bespalov
Deposited On:08 October 2010

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