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

doi:10.1137/S0036142900378406

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 publication › Journal article › Academic research › peer-review

46 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 language	English
Pages (from-to)	1538-1560
Number of pages	23
Journal	SIAM Journal on Numerical Analysis
Volume	40
Issue number	4
DOIs	https://doi.org/10.1137/S0036142900378406
Publication status	Published - 1 Sept 2002
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Numerical Analysis

More information

10.1137/S0036142900378406

Cite this

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

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.",

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T1 - Sharp L2-error estimates and superconvergence of mixed finite element methods for non-fickian flows in porous media

AU - Ewing, Richard E.

AU - Lin, Yanping

AU - Sun, Tong

AU - Wang, Junping

AU - Zhang, Shuhua

PY - 2002/9/1

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N2 - 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.

AB - 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.

KW - Error estimates

KW - Mixed finite element methods

KW - Mixed Ritz-Volterra projection

KW - Non-Fickian flow

KW - Superconvergence

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