{"paper":{"title":"Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bernardo Cockburn, Kassem Mustapha, Maher Nour","submitted_at":"2014-12-05T18:42:23Z","abstract_excerpt":"We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\\alpha<1$. For each time $t \\in [0,T]$, the HDG approximations are taken to be piecewise polynomials of degree $k\\ge0$ on the spatial domain~$\\Omega$, the approximations to the exact solution $u$ in the $L_\\infty\\bigr(0,T;L_2(\\Omega)\\bigr)$-norm and to $\\nabla u$ in the $L_\\infty\\bigr(0,T;{\\bf L}_2(\\Omega)\\bigr)$-norm are proven to converge with the rate $h^{k+1}$ provided that $u$ is sufficiently regular, where $h$ is the maximum d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2098","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"}