{"paper":{"title":"Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Rongchan Zhu, Ting Ma","submitted_at":"2019-08-25T14:03:16Z","abstract_excerpt":"In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on $\\T$. First we prove that the convergence rate for stochastic 2D heat equation is of order $\\alpha-\\delta$ in Besov space $\\C^{-\\alpha}$ for $\\alpha\\in(0,1)$ and $\\delta>0$ arbitrarily small. Then we obtain the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations of order $\\alpha-\\delta$ in $\\C^{-\\alpha}$ for $\\alpha\\in(0,2/9)$ and $\\delta>0$ arbitrarily small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09331","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/1908.09331/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"}