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 Γ. 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 Γ. We establish quasioptimal 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.
Original languageEnglish
Number of pages25
JournalNumerische Mathematik
Volume132
Issue number4
Early online date21 Jun 2015
DOIs
Publication statusPublished - 21 Jun 2015

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-015-0736-3

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