{"paper":{"title":"Regularity of the diffusion-dispersion tensor and error analysis of Galerkin FEMs for a porous media flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Buyang Li, Weiwei Sun","submitted_at":"2014-06-13T12:02:04Z","abstract_excerpt":"We study Galerkin finite element methods for an incompressible miscible flow in porous media with the commonly-used Bear-Scheidegger diffusion-dispersion tensor $D({\\bf u}) = \\Phi d_m I + |{\\bf u}| \\big ( \\alpha_T I + (\\alpha_L - \\alpha_T) \\frac{{\\bf u} \\otimes {\\bf u}}{|{\\bf u}|^2}\\big)$. The traditional approach to optimal $L^\\infty((0,T);L^2)$ error estimates is based on an elliptic Ritz projection, which usually requires the regularity of $\\nabla_x\\partial_tD({\\bf u}(x,t)) \\in L^p(\\Omega_T)$. However, the Bear-Scheidegger diffusion-dispersion tensor may not satisfy the regularity condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3515","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"}