{"paper":{"title":"(In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexander Shapeev, Christoph Ortner, Lei Zhang","submitted_at":"2013-08-18T20:20:51Z","abstract_excerpt":"We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c coupling as well as a stabilisation mechanism for unstable coupling schemes.\n  We then present a comprehensive study of a two-dimensional scalar planar interface setting, as a step towards a general 2D/3D vectorial analysis. Our results point out various new challenges. For example, we find that none of the ghost force-free methods known to us are universally stable (i.e., stable under general interaction and general l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3894","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"}