{"paper":{"title":"$L^\\infty$- and $W^{1,\\infty}$-error estimates of linear finite element method for Neumann boundary value problems in a smooth domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Takahito Kashiwabara, Tomoya Kemmochi","submitted_at":"2018-04-02T03:54:05Z","abstract_excerpt":"Pointwise error analysis of the linear finite element approximation for $-\\Delta u + u = f$ in $\\Omega$, $\\partial_n u = \\tau$ on $\\partial\\Omega$, where $\\Omega$ is a bounded smooth domain in $\\mathbb R^N$, is presented. We establish $O(h^2|\\log h|)$ and $O(h)$ error bounds in the $L^\\infty$- and $W^{1,\\infty}$-norms respectively, by adopting the technique of regularized Green's functions combined with local $H^1$- and $L^2$-estimates in dyadic annuli. Since the computational domain $\\Omega_h$ is only polyhedral, one has to take into account non-conformity of the approximation caused by the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00390","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"}