# The BEM with graded meshes for the electric field integral equation on polyhedral surfaces

Abstract : We consider the variational formulation of the electric field integral equation on a Lipschitz polyhedral surface $$\Gamma$$. We study the Galerkin boundary element discretisations based on the lowest-order Raviart–Thomas surface elements on a sequence of anisotropic meshes algebraically graded towards the edges of $$\Gamma$$. We establish quasi-optimal convergence of Galerkin solutions under a mild restriction on the strength of grading. The key ingredient of our convergence analysis are new componentwise stability properties of the Raviart–Thomas interpolant on anisotropic elements.
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### Citation

A. Bespalov, Serge Nicaise. The BEM with graded meshes for the electric field integral equation on polyhedral surfaces. Numerische Mathematik, Springer Verlag, 2016, 132 (4), pp.631-655. ⟨10.1007/s00211-015-0736-3⟩. ⟨hal-03135588⟩

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