{"paper":{"title":"Interior numerical approximation of boundary value problems with a distributional data","license":"","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Ivo Babuska, Victor Nistor","submitted_at":"2004-10-06T20:29:45Z","abstract_excerpt":"We study the approximation properties of a harmonic function $u \\in H\\sp{1-k}(\\Omega)$, $k > 0$, on relatively compact sub-domain $A$ of $\\Omega$, using the Generalized Finite Element Method. For smooth, bounded domains $\\Omega$, we obtain that the GFEM--approximation $u_S$ satisfies $\\|u - u_S\\|_{H\\sp{1}(A)} \\le C h^{\\gamma}\\|u\\|_{H\\sp{1-k}(\\Omega)}$, where $h$ is the typical size of the ``elements'' defining the GFEM--space $S$ and $\\gamma \\ge 0 $ is such that the local approximation spaces contain all polynomials of degree $k + \\gamma + 1$. The main technical result is an extension of the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410184","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0410184/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}