{"paper":{"title":"Maximum norm error estimates for the finite element approximation of parabolic problems on smooth domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Takahito Kashiwabara, Tomoya Kemmochi","submitted_at":"2018-05-03T14:47:55Z","abstract_excerpt":"In this paper, we consider the finite element approximation for a parabolic problem on a smooth domain $\\Omega \\subset \\mathbb{R}^N$ with the inhomogeneous Neumann boundary condition. We emphasize that the domain can be non-convex in general. We implement the finite element method for this problem by constructing a family of polygonal or polyhedral domains $\\{ \\Omega_h \\}_h$ that approximate the original domain $\\Omega$. The main result of this study is the $L^\\infty$-error estimate for this approximation. We shall show that the convergence rate is not optimal for higher order elements since t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01336","kind":"arxiv","version":2},"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"}