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

Wentao Cai, Buyang Li, Yanping Lin, Weiwei Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

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 ∇ 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 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.

Original languageEnglish
Pages (from-to)1009-1042
Number of pages34
JournalNumerische Mathematik
Volume141
Issue number4
DOIs
Publication statusPublished - 28 Feb 2019

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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