{"paper":{"title":"Numerical resolution of an anisotropic non-linear diffusion problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexandre Mouton (LPP), Fabrice Deluzet (IMT), St\\'ephane Brull (MAB)","submitted_at":"2012-10-02T07:44:40Z","abstract_excerpt":"This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \\varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit \\varepsilon \\infty 0 is demonstrated to be a singular perturbation of the original diffusion equation. To address efficiently this problem, an Asymptotic-Preserving scheme is derived. This numerical method does not require the use of coordinates adapted to the aniso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0681","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"}