Analysis of fully discrete FEM for miscible displacement in porous media with Bear–Scheidegger diffusion tensor

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1009-1042
Journal / PublicationNumerische Mathematik
Volume141
Issue number4
Online published28 Feb 2019
Publication statusPublished - Apr 2019

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)uu|u|2). Previous works on optimal-order L (0 , T; L2)-norm error estimate required the regularity assumption ∇xt 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 Lp-regularity of fully discrete finite element solutions of parabolic equations, optimal error estimate in Lp (0 , T; Lq)-norm and almost optimal error estimate in L (0 , T; Lq)-norm are established under the assumption of D(u) being Lipschitz continuous with respect to u.

Citation Format(s)

Analysis of fully discrete FEM for miscible displacement in porous media with Bear–Scheidegger diffusion tensor. / Cai, Wentao; Li, Buyang; Lin, Yanping et al.
In: Numerische Mathematik, Vol. 141, No. 4, 04.2019, p. 1009-1042.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review