{"paper":{"title":"A quasi-optimal variant of the Hybrid High-Order method for elliptic PDEs with $H^{-1}$ loads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexandre Ern, Pietro Zanotti","submitted_at":"2019-04-30T09:50:06Z","abstract_excerpt":"Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space $L^2(\\Omega)$. In this paper we devise and analyze a variant thereof, which is defined for any load in the dual Sobolev space $H^{-1}(\\Omega)$. The main feature of the present variant is that its $H^1$-norm error can be bounded only in terms of the $H^1$-norm best error in a space of broken polynomials. We establish this estimate with the help of recent results on the quasi-optimality of nonconforming methods. We prove also an improved error bound in the $L^2$-norm by duali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13125","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"}