{"paper":{"title":"$L^{2}$-Discretization Error Bounds for Maps into Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hanne Hardering","submitted_at":"2016-12-19T09:19:55Z","abstract_excerpt":"We study the approximation of functions that map a Euclidean domain $\\Omega\\subset \\mathbb{R}^{d}$ into an $n$-dimensional Riemannian manifold $(M,g)$ minimizing an elliptic, semilinear energy in a function set $H\\subset W^{1,2}(\\Omega,M)$. The approximation is given by a restriction of the energy minimization problem to a family of conforming finite-dimensional approximations $S_{h}\\subset H$. We provide a set of conditions on $S_{h}$ such that we can prove a priori $W^{1,2}$- and $L^{2}$-approximation error estimates comparable to standard Euclidean finite elements. This is done in an intrin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06086","kind":"arxiv","version":2},"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"}