L-Error estimates and superconvergence in maximum norm of mixed finite element methods for nonfickian flows in porous media

Richard E. Ewing, Yanping Lin, Junping Wang, Shuhua Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

20 Citations (Scopus)

Abstract

On the basis of the estimates for the regularized Green’s functions with memory terms, optimal order L∞-error estimates are established for the nonFickian flow of fluid in porous media by means of a mixed Ritz-Volterra projection. Moreover, local L∞-superconvergence estimates for the velocity along the Gauss lines and for the pressure at the Gauss points are derived for the mixed finite element method, and global L∞-superconvergence estimates for the velocity and the pressure are also investigated by virtue of an interpolation post-processing technique. Meanwhile, some useful a-posteriori error estimators are presented for this mixed finite element method.
Original languageEnglish
Pages (from-to)301-328
Number of pages28
JournalInternational Journal of Numerical Analysis and Modeling
Volume2
Issue number3
Publication statusPublished - 1 Jan 2005
Externally publishedYes

Keywords

  • Error estimates and superconvergence
  • Green’s functions
  • Mixed finite element methods
  • Nonfickian flow
  • The mixed ritz- volterra projection

ASJC Scopus subject areas

  • Numerical Analysis

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