Regularity of the diffusion-dispersion tensor and error analysis of Galerkin FEMS for a porous medium flow

Buyang Li, Weiwei Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)

Abstract

We study Galerkin finite element methods for an incompressible miscible flow in porous media with the commonly used Bear-Scheidegger diffusion-dispersion tensor {equation presented} The traditional approach to optimal L((0, T);L2) error estimates is based on an elliptic Ritz projection, which usually requires the regularity of ?x?tD(u(x, t)) ∈Lp(ΩT ). However, the Bear-Scheidegger diffusion-dispersion tensor may not satisfy the regularity condition even for a smooth velocity field u. A new approach is presented in this paper, in terms of a parabolic projection, which only requires the Lipschitz continuity of D(u). With the new approach, we establish optimal Lp error estimates and an almost optimal L error estimate.
Original languageEnglish
Pages (from-to)1418-1437
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume53
Issue number3
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

Keywords

  • Diffusion-dispersion tensor
  • Error analysis
  • Galerkin FEM
  • Lp stability
  • Parabolic projection
  • Porous medium flow

ASJC Scopus subject areas

  • Numerical Analysis

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