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.
https://hal-uphf.archives-ouvertes.fr/hal-03135588 Contributor : Julie CagniardConnect in order to contact the contributor Submitted on : Tuesday, July 5, 2022 - 5:08:43 PM Last modification on : Friday, July 8, 2022 - 2:48:46 PM
A. Bespalov, Serge Nicaise. The BEM with graded meshes for the electric field integral equation on polyhedral surfaces. Numerische Mathematik, Springer Verlag, 2016, 132 (4), pp.631-655. ⟨10.1007/s00211-015-0736-3⟩. ⟨hal-03135588⟩