{"paper":{"title":"An unconditionally stable discontinuous Galerkin method for the elastic Helmholtz equations with large frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Cody Lorton, Xiaobing Feng","submitted_at":"2015-01-21T22:01:17Z","abstract_excerpt":"In this paper we propose and analyze an interior penalty discontinuous Galerkin (IP-DG) method using piecewise linear polynomials for the elastic Helmholtz equations with the first order absorbing boundary condition. It is proved that the sesquilinear form for the problem satisfies a generalized weak coercivity property, which immediately infers a stability estimate for the solution of the differential problem in all frequency regimes. It is also proved that the proposed IP-DG method is unconditionally stable with respect to both frequency $\\omega$ and mesh size $h$. Sub-optimal order (with re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05340","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"}