{"paper":{"title":"A Hierarchical A-Posteriori Error Estimatorfor the Reduced Basis Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Karsten Urban, Mario Ohlberger, Mladjan Radic, Stefan Hain","submitted_at":"2018-02-09T15:09:12Z","abstract_excerpt":"In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\\inf$-$\\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a Petrov-Galerkin framework, where the reduced approximation spaces are constructed by the (weak) Greedy algorithm. We propose and analyze a hierarchical a posteriori error estimator which evaluates the difference of two reduced approximations of different accuracy. Based on the a priori error analysis of the (weak) Greedy algorithm, it is expected that the hie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03298","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"}