{"paper":{"title":"Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Rob Falgout, Shun Zhang, Zhiqiang Cai","submitted_at":"2014-07-17T05:12:25Z","abstract_excerpt":"The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficiency of the L2 norm first-order system least-squares (FOSLS) ap- proach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach in [10] was applied to the div-curl system with added slack vari- ables, and hence it is quite complicated. In this paper, we apply the FOSLL* approach to the div system and establish its well-posedness. For the corresponding finite ele- ment approximation, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4558","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"}