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 $$\Gamma $$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 $$\Gamma $$Γ. 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.