2015/04/10 by Bespalov, Alex, Nicaise, Serge
#65N12 #65N38 #78M15 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1504.02647
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 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.