{"paper":{"title":"The Heterogeneous Multiscale Finite Element Method for the Homogenization of Linear Elastic Solids and a Comparison with the FE$^2$ Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andreas Fischer, Bernhard Eidel","submitted_at":"2017-01-28T18:58:10Z","abstract_excerpt":"The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \\emph{Commun. Math. Sci.}, 1 (2003), 87--132]. The objective of the present work is an FE-HMM formulation for the homogenization of linear elastic solids in a geometrical linear frame, and doing so, for the first time, of a vector-valued field problem. A key ingredient of FE-HMM is that macrostiffness is estimated by stiffness sampling on heterogeneous microdomains in terms a of modif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08313","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"}