Sharp L2-error estimates and superconvergence of mixed finite element methods for non-fickian flows in porous media

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

38 Citations (Scopus)

Abstract

A sharper L2-error estimate is obtained for the non-Fickian flow of fluid in porous media by means of a mixed Ritz-Volterra projection instead of the mixed Ritz projection used in [R. E. Ewing, Y. Lin, and J. Wang, Acta Math. Univ. Comenian. (N.S.), 70 (2001), pp. 75-84]. Moreover, local L2superconvergence for the velocity along the Gauss lines and for the pressure at the Gauss points is derived for the mixed finite element method via the Ritz-Volterra projection, and global L2superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique. On the basis of the superconvergence estimates, some useful a posteriori error estimators are presented for this mixed finite element method.
Original languageEnglish
Pages (from-to)1538-1560
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume40
Issue number4
DOIs
Publication statusPublished - 1 Sep 2002
Externally publishedYes

Keywords

  • Error estimates
  • Mixed finite element methods
  • Mixed Ritz-Volterra projection
  • Non-Fickian flow
  • Superconvergence

ASJC Scopus subject areas

  • Numerical Analysis

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