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We show in the case $n=1$ (i.e. the evolving hypersurfaces are curves), that"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.2392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-11T13:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"f52c192f1a7fe683a82ac0690a9b6d4ebc3d970f8d01bc89a55536e56ca98ffa","abstract_canon_sha256":"f64007a9e5c96491da2c64bbe1291002e9c79948b70cd942015b9b5a06b0ecd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:07.564162Z","signature_b64":"oVp3dH4bzW/4A5Ql/jPaErEYR2cXbKtYhHLu+6TDokqF2u4c5boQLAEeUvslxadTO8P1IToT+tqCX3qbZM9cBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cc16a26c0a7eb7eae00110c557eb858270b47f5ce41ebb0f6286721502ed559","last_reissued_at":"2026-05-18T03:16:07.563313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:07.563313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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