{"paper":{"title":"An absolutely stable $hp$-HDG method for the time-harmonic Maxwell equations with high wave number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Huangxin Chen, Peipei Lu, Weifeng Qiu","submitted_at":"2015-03-26T11:50:11Z","abstract_excerpt":"We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem becomes the solution of a mixed curl-curl formulation of the Maxwell's problem. The method is shown to be an absolutely stable HDG method for the indefinite time-harmonic Maxwell equations with high wave number. By exploiting the duality argument, the dependence of convergence of the HDG method on the wave number k, the mesh size h and the polynomial order p i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07696","kind":"arxiv","version":3},"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"}