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

Bespalov, Alexei and Heuer, Norbert (2010) Natural hp-BEM for the electric field integral equation with singular solutions. [MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 41 Approximations and expansions
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
Depositing User: Alex Bespalov
Date Deposited: 08 Oct 2010
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1529

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