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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

3 Scopus Citations
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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.