{"paper":{"title":"Local Error Estimates of the Finite Element Method for an Elliptic Problem with a Dirac Source Term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Astrid Decoene (LM-Orsay), Lo\\\"ic Lacouture (LM-Orsay), S\\'ebastien Martin (MAP5), Silvia Bertoluzza","submitted_at":"2015-05-12T14:42:39Z","abstract_excerpt":"The solutions of elliptic problems with a Dirac measure in right-hand side are not H1 and therefore the convergence of the finite element solutions is suboptimal. Graded meshes are standard remedy to recover quasi-optimality, namely optimality up to a log-factor, for low order finite elements in L2-norm. Optimal (or quasi-optimal for the lowest order case) convergence has been shown in L2-seminorm, where the L2-seminorm is defined as the L2-norm on a subdomain which excludes the singularity. Here we show a quasi-optimal convergence for the Hs-seminorm, s \\textgreater{} 0, and an optimal conver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03032","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"}