{"paper":{"title":"Superconvergent HDG methods for Maxwell's equations via the $M$-decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gang Chen, Peter Monk, Yangwen Zhang","submitted_at":"2019-05-17T17:30:38Z","abstract_excerpt":"The concept of the $M$-decomposition was introduced by Cockburn et al.\\ in Math. Comp.\\ vol.\\ 86 (2017), pp.\\ 1609-1641 {to provide criteria to guarantee optimal convergence rates for the Hybridizable Discontinuous Galerkin (HDG) method for coercive elliptic problems}. In that paper they systematically constructed superconvergent hybridizable discontinuous Galerkin (HDG) methods to approximate the solutions of elliptic PDEs on unstructured meshes. In this paper, we use the $M$-decomposition to construct HDG methods for the Maxwell's equations on unstructured meshes in two dimension. In particu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07383","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"}