{"paper":{"title":"Unconditionally optimal error estimates of a Crank--Nicolson Galerkin method for the nonlinear thermistor equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Buyang Li, Weiwei Sun","submitted_at":"2012-11-08T10:01:11Z","abstract_excerpt":"This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank--Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in $d$-dimensional space, $d=2,3$. We split the error function into two parts, one from the spatial discretization and one from the temporal discretization, by introducing a corresponding time-discrete (elliptic) system. We present a rigorous analysis for the regularity of the solution of the time-discrete system and error estimates of the time discretization. With these estimates and the proved regulari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1809","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"}