{"paper":{"title":"Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Guillaume Bal, Wenjia Jing","submitted_at":"2012-09-22T09:19:36Z","abstract_excerpt":"This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. We show that the random fluctuations of such solutions are correctly estimated by the heterogeneous multi-scale algorithm when appropriate fine-scale problems are solved on subsets that cover the whole computational domain. However, when the fine-scale problems are solved over patches that do not cover the entire domain, the random fluctuations may or may not be estimated accurately. In the case of random potentials w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4974","kind":"arxiv","version":2},"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"}