{"paper":{"title":"Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dirk Praetorius, Jens Markus Melenk, Markus Aurada, Michael Feischl, Michael Karkulik, Thomas F\\\"uhrer","submitted_at":"2012-11-18T15:35:53Z","abstract_excerpt":"We consider a (possibly) nonlinear interface problem in 2D and 3D, which is solved by use of various adaptive FEM-BEM coupling strategies, namely the Johnson-N\\'ed\\'elec coupling, the Bielak-MacCamy coupling, and Costabel's symmetric coupling. We provide a framework to prove that the continuous as well as the discrete Galerkin solutions of these coupling methods additionally solve an appropriate operator equation with a Lipschitz continuous and strongly monotone operator. Therefore, the coupling formulations are well-defined, and the Galerkin solutions are quasi-optimal in the sense of a C\\'ea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4225","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"}