A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces

Alex Bespalov, Serge Nicaise

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Abstract

The Galerkin boundary element discretisations of the electric field integral equation (EFIE) on Lipschitz polyhedral surfaces suffer slow convergence rates when the underlying surface meshes are quasi-uniform and shape-regular. This is due to singular behaviour of the solution to this problem in neighbourhoods of vertices and edges of the surface. Aiming to improve convergence rates of the Galerkin boundary element method (BEM) for the EFIE on a Lipschitz polyhedral closed surface Γ, we employ anisotropic meshes algebraically graded towards the edges of Γ. We prove that on sufficiently graded meshes the h-version of the BEM with the lowest-order Raviart-Thomas elements regains (up to a small order of ε) an optimal convergence rate (i.e., the rate of the h-BEM on quasi-uniform meshes for smooth solutions).
Original languageEnglish
Pages (from-to)1636-1644
Number of pages9
JournalComputers & Mathematics with Applications
Volume71
Issue number8
Early online date28 Mar 2016
DOIs
Publication statusPublished - Apr 2016

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