{"paper":{"title":"Recovery based finite element method for biharmonic equation in two dimensional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Huayi Wei, Nianyu Yi, Wei Yang, Yunqing Huang","submitted_at":"2018-06-14T08:56:45Z","abstract_excerpt":"We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation. The main idea is to replace the gradient operator $\\nabla$ on linear finite element space by $G(\\nabla)$ in the weak formulation of the biharmonic equation, where $G$ is the recovery operator which recovers the piecewise constant function into the linear finite element space. By operator $G$, Laplace operator $\\Delta$ is replaced by $\\nabla\\cdot G(\\nabla)$. Furthermore the boundary condition on normal derivative $\\nabla u\\cdot \\pmb{n}$ is treated by the boundary penalty method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05417","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"}