{"paper":{"title":"Finite element approximation of power mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Heiko Kr\\\"oner","submitted_at":"2013-08-11T13:17:08Z","abstract_excerpt":"In [21] the evolution of hypersurfaces in $\\mathbb{R}^{n+1}$ with normal speed equal to a power $k>1$ of the mean curvature is considered and the levelset solution $u$ of the flow is obtained as the $C^0$-limit of a sequence $u^{\\epsilon}$ of smooth functions solving the regularized levelset equations.\n  We prove a rate for this convergence.\n  Then we triangulate the domain by using a tetraeder mesh and consider continuous finite elements, which are polynomials of degree $\\le 2$ on each tetraeder of the triangulation. We show in the case $n=1$ (i.e. the evolving hypersurfaces are curves), that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2392","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"}