{"paper":{"title":"Maximum principle in linear finite element approximations of anisotropic diffusion-convection-reaction problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Changna Lu, Jianxian Qiu, Weizhang Huang","submitted_at":"2012-01-17T17:22:51Z","abstract_excerpt":"A mesh condition is developed for linear finite element approximations of anisotropic diffusion-convection-reaction problems to satisfy a discrete maximum principle. Loosely speaking, the condition requires that the mesh be simplicial and $\\mathcal{O}(\\|\\V{b}\\|_\\infty h + \\|c\\|_\\infty h^2)$-nonobtuse when the dihedral angles are measured in the metric specified by the inverse of the diffusion matrix, where $h$ denotes the mesh size and $\\V{b}$ and $c$ are the coefficients of the convection and reaction terms. In two dimensions, the condition can be replaced by a weaker mesh condition (an $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3564","kind":"arxiv","version":3},"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"}