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Journal Articles Numerische Mathematik Year : 2016

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

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A. Bespalov
• Function : Author
Serge Nicaise
• Function : Author
• PersonId : 1080829

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.

Domains

Mathematics [math]

Dates and versions

hal-03135588 , version 1 (05-07-2022)

Identifiers

• HAL Id : hal-03135588 , version 1
• DOI :

Cite

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

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