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http://hdl.handle.net/10397/89360
| Title: | Analysis of fully discrete FEM for miscible displacement in porous media with Bear–Scheidegger diffusion tensor | Authors: | Cai, W Li, B Lin, Y Sun, W |
Issue Date: | Apr-2019 | Source: | Numerische mathematik, Apr. 2019, v. 141, no. 4, p. 1009-1042 | Abstract: | 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(u)=γdmI+|u|(αTI+(αL-αT)u⊗u|u|2).Previous works on optimal-order L ∞ (0 , T; L 2 ) -norm error estimate required the regularity assumption ∇ x ∂ t D(u(x, t)) ∈ L ∞ (0 , T; L ∞ (Ω)) , while the Bear–Scheidegger diffusion–dispersion tensor is only Lipschitz continuous even for a smooth velocity field u. In terms of the maximal L p -regularity of fully discrete finite element solutions of parabolic equations, optimal error estimate in L p (0 , T; L q ) -norm and almost optimal error estimate in L ∞ (0 , T; L q ) -norm are established under the assumption of D(u) being Lipschitz continuous with respect to u. | Publisher: | Springer | Journal: | Numerische mathematik | ISSN: | 0029-599X | EISSN: | 0945-3245 | DOI: | 10.1007/s00211-019-01030-0 | Rights: | © Springer-Verlag GmbH Germany, part of Springer Nature 2019 This is a post-peer-review, pre-copyedit version of an article published in Numerische Mathematik. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00211-019-01030-0 |
| Appears in Collections: | Journal/Magazine Article |
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