{"paper":{"title":"Stable Finite Element Methods Preserving $\\nabla \\cdot \\boldsymbol{B} = 0$ Exactly for MHD Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jinchao Xu, Kaibo Hu, Yicong Ma","submitted_at":"2014-10-04T21:28:27Z","abstract_excerpt":"This paper is devoted to the design and analysis of some structure-preserving finite element schemes for the magnetohydrodynamics (MHD) system. The main feature of the method is that it naturally preserves the important Gauss law, namely $\\nabla\\cdot\\boldsymbol{B}=0$. In contrast to most existing approaches that eliminate the electrical field variable $\\boldsymbol{E}$ and give a direct discretization of the magnetic field, our new approach discretizes the electric field $\\boldsymbol{E}$ by N\\'{e}d\\'{e}lec type edge elements for $H(\\mathrm{curl})$, while the magnetic field $\\boldsymbol{B}$ by R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1095","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"}