{"paper":{"title":"Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.flu-dyn","authors_text":"Dmitry Kolomenskiy, Kai Schneider, Romain Nguyen van yen","submitted_at":"2012-05-31T09:59:52Z","abstract_excerpt":"We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\\eta$, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of $\\eta$, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed $\\eta$, we find that only the part of the spectrum corresponding to eigenvalues $\\lambda \\lesssim \\eta^{-1}$ approaches Dirich"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0002","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"}