Skip to Main content Skip to Navigation
Journal articles

A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces

Abstract : The Galerkin boundary element discretisations of the electric field integral equation (EFIE) on Lipschitz polyhedral surfaces suffer slow convergence rates when the underlying surface meshes are quasi-uniform and shape-regular. This is due to singular behaviour of the solution to this problem in neighbourhoods of vertices and edges of the surface. Aiming to improve convergence rates of the Galerkin boundary element method (BEM) for the EFIE on a Lipschitz polyhedral closed surface Γ, we employ anisotropic meshes algebraically graded towards the edges of Γ. We prove that on sufficiently graded meshes the h-version of the BEM with the lowest-order Raviart–Thomas elements regains (up to a small order of ε>0) an optimal convergence rate (i.e., the rate of the h-BEM on quasi-uniform meshes for smooth solutions).
Document type :
Journal articles
Complete list of metadata

https://hal-uphf.archives-ouvertes.fr/hal-03135595
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Tuesday, February 9, 2021 - 10:06:13 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

Links full text

Identifiers

Collections

Citation

A. Bespalov, Serge Nicaise. A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces. Computers & Mathematics with Applications, Elsevier, 2016, 71 (8), pp.1636-1644. ⟨10.1016/j.camwa.2016.03.013⟩. ⟨hal-03135595⟩

Share

Metrics

Record views

22