{"paper":{"title":"Divergence-free H(div)-conforming hierarchical bases for magnetohydrodynamics (MHD)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.plasm-ph"],"primary_cat":"math.NA","authors_text":"Jianguo Xin, Jian Wu, Wei Cai","submitted_at":"2012-10-20T03:20:34Z","abstract_excerpt":"In order to solve the magnetohydrodynamics (MHD) equations with a $\\mathbf{\\mathcal{H}}(\\mathbf{div})$-conforming element, a novel approach is proposed to ensure the exact divergence-free condition on the magnetic field. The idea is to add on each element an extra interior bubble function from higher order hierarchical $\\mathbf{\\mathcal{H}}(\\mathbf{div})$-conforming basis. Four such hierarchical bases for the $\\mathbf{\\mathcal{H}}% (\\mathbf{div})$-conforming quadrilateral, triangular, hexahedral and tetrahedral elements are either proposed (in the case of tetrahedral) or reviewed. Numerical re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5575","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"}