{"paper":{"title":"Analysis of fully discrete FEM for miscible displacement in porous media with Bear--Scheidegger diffusion tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Buyang Li, Weiwei Sun, Wentao Cai, Yanping Lin","submitted_at":"2018-09-10T11:31:08Z","abstract_excerpt":"Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear--Scheidegger diffusion-dispersion tensor: $$ D({\\bf u}) = \\gamma d_m I + |{\\bf u}|\\bigg( \\alpha_T I + (\\alpha_L - \\alpha_T) \\frac{{\\bf u} \\otimes {\\bf u}}{|{\\bf u}|^2}\\bigg) \\, . $$ Previous works on optimal-order $L^\\infty(0,T;L^2)$-norm error estimate required the regularity assumption $\\nabla_x\\partial_tD({\\bf u}(x,t)) \\in L^\\infty(0,T;L^\\infty(\\Omega))$, while the Bear--Scheidegger diffusion-dispersion tensor is only Lipschitz continuous even for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03240","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"}