{"paper":{"title":"A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"J. Dick, K. Mustapha, Q. T. Le Gia, W. McLean","submitted_at":"2024-07-09T13:02:53Z","abstract_excerpt":"Due to the divergence-instability, the accuracy of low-order conforming finite element methods (FEMs) for nearly incompressible elasticity equations deteriorates as the Lam\\'e parameter $\\lambda\\to\\infty$, or equivalently as the Poisson ratio $\\nu\\to1/2$. This effect is known as {\\itshape locking} or {\\itshape non-robustness}. For the piecewise linear case, the error in the ${\\bf L}^2$-norm of the standard Galerkin conforming FEM is bounded by~$C\\lambda h^2$, resulting in poor accuracy for practical values of~$h$ if $\\lambda$ is sufficiently large. In this short paper, we show that the locking"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06831","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.06831/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}