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)

129 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

Bibliographical note

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

Access to Document

10.1007/s00211-015-0736-3

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
Accepted author manuscript, 235 KBLicence: Other (please specify with Rights Statement)

http://dx.doi.org/10.1007/s00211-015-0736-3

Cite this

@article{fb1c212220ff4167898838e273b86d7f,

title = "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 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.",

author = "Alex Bespalov and Serge Nicaise",

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

year = "2015",

month = jun,

day = "21",

doi = "10.1007/s00211-015-0736-3",

language = "English",

volume = "132",

journal = "Numerische Mathematik",

issn = "0029-599X",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - The BEM with graded meshes for the electric field integral equation on polyhedral surfaces

AU - Bespalov, Alex

AU - Nicaise, Serge

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-015-0736-3

PY - 2015/6/21

Y1 - 2015/6/21

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.

U2 - 10.1007/s00211-015-0736-3

DO - 10.1007/s00211-015-0736-3

M3 - Article

SN - 0029-599X

VL - 132

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 4

ER -

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

Abstract

Bibliographical note

Access to Document

Fingerprint

Cite this