{"paper":{"title":"The BEM with graded meshes for the electric field integral equation on polyhedral surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alex Bespalov, Serge Nicaise","submitted_at":"2015-04-10T12:02:23Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02647","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}