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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.3515","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-13T12:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"ab866a962b6bfcd49d14e530545ae805d07b488d60cd9df63aa5d11857bb11f3","abstract_canon_sha256":"8853b0f63a35676be46fbe0b090736000e6e9290b7e002cf2b4751e684359615"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:46.525246Z","signature_b64":"mCsjOYVcLdDC3X/EmIoTyqHAciSgO+jnzeqj7PAQxYzHNq97cqId6BheF5orD9pl8wbtYJcW2+aklYGnDx+5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d78e7d5e08588b281a46892c874104fb677b7686e960618b8bdedffa94c09d9b","last_reissued_at":"2026-05-18T02:49:46.524879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:46.524879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\nabla_x\\partial_tD({\\bf u}(x,t)) \\in L^p(\\Omega_T)$. 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