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arXiv · 1504.02647

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

Alex Bespalov·Serge Nicaise
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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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Alex Bespalov, Serge Nicaise. 2015-04-10. The BEM with graded meshes for the electric field integral equation on polyhedral surfaces. https://arxiv.org/abs/1504.02647

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