{"paper":{"title":"Error analysis of a finite volume element method for fractional order evolution equations with nonsmooth initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amiya K. Pani, Samir Karaa","submitted_at":"2017-02-12T03:54:38Z","abstract_excerpt":"In this paper, a finite volume element (FVE) method is considered for spatial approximations of time-fractional diffusion equations involving a Riemann-Liouville fractional derivative of order $\\alpha \\in (0,1)$ in time. Improving upon earlier results (Karaa {\\it et al.}, IMA J. Numer. Anal. 2016), optimal error estimates in $L^2(\\Omega)$- and $H^1(\\Omega)$-norms for the semidiscrete problem with smooth and middly smooth initial data, i.e., $v\\in H^2(\\Omega)\\cap H^1_0(\\Omega)$ and $v\\in H^1_0(\\Omega)$ are established. For nonsmooth data, that is, $v\\in L^2(\\Omega)$, the optimal $L^2(\\Omega)$-e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03485","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"}