{"paper":{"title":"A Finite Element Framework for Some Mimetic Finite Difference Discretizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carmen Rodrigo, Francisco Gaspar, Ludmil Zikatanov, Xiaozhe Hu","submitted_at":"2015-03-15T13:12:53Z","abstract_excerpt":"In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified N\\'ed\\'elec-Raviart-Thomas finite element methods for model problems in $\\mathbf{H}(\\operatorname{\\mathbf{curl}})$ and $H(\\operatorname{div})$. This provides a simple and transparent way to analyze such mimetic finite difference discretizations using the well-known results from finite element theory. The finite element framework that we develop is also crucial for the design of efficient multigrid methods for mimetic finite difference discretizations, since it allows us to us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04423","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"}