{"paper":{"title":"Uniform Error Estimation for Convection-Diffusion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Sebastian Franz","submitted_at":"2014-03-03T12:22:18Z","abstract_excerpt":"Let us consider the singularly perturbed model problem $Lu:=-\\varepsilon\\Delta u-bu_x+c u =f$ with homogeneous Dirichlet boundary conditions on $\\Gamma=\\partial\\Omega$ $u|_\\Gamma =0$ on the unit-square $\\Omega=(0,1)^2$. Assuming that $b>0$ is of order one, the small perturbation parameter $0<\\varepsilon\\ll 1$ causes boundary layers in the solution. In order to solve above problem numerically, it is beneficial to resolve these layers. On properly layer-adapted meshes we can apply finite element methods and observe convergence.\n  We will consider standard Galerkin and stabilised FEM applied to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0407","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"}