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

Alex Bespalov; Serge Nicaise

doi:10.1007/s00211-015-0736-3

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

Alex Bespalov
, Serge Nicaise

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

214 Downloads (Pure)

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 language	English
Number of pages	25
Journal	Numerische Mathematik
Volume	132
Issue number	4
Early online date	21 Jun 2015
DOIs	https://doi.org/10.1007/s00211-015-0736-3
Publication status	Published - 21 Jun 2015

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

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Bespalov_Nicaise_BEM_Graded_Meshes_Numerische_Mathematik_2015
The final publication is available at Springer via: http://dx.doi.org/10.1007/s00211-015-0736-3. Eligibility for repository checked July 2015
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http://dx.doi.org/10.1007/s00211-015-0736-3

Cite this

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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.",

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AU - Nicaise, Serge

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N2 - 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.

AB - 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.

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VL - 132

JO - Numerische Mathematik

JF - Numerische Mathematik

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

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