{"paper":{"title":"A Priori and A Posteriori Error Control of Discontinuous Galerkin Finite Element Methods for the Von K\\'arm\\'an Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carsten Carstensen, Gouranga Mallik, Neela Nataraj","submitted_at":"2017-08-25T17:24:05Z","abstract_excerpt":"This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von K\\'arm\\'an equations defined on a polygonal domain. A discrete inf-sup condition sufficient for the stability of the discontinuous Galerkin discretization of a well-posed linear problem is established and this allows the proof of local existence and uniqueness of a discrete solution to the non-linear problem with a Banach fixed point theorem. The Newton scheme is locally second-order convergent and appears to be a robust solution strategy up to machine precision. A comprehensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07815","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"}