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

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 publication › Journal article › Academic research › peer-review

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 language	English
Pages (from-to)	301-328
Number of pages	28
Journal	International Journal of Numerical Analysis and Modeling
Volume	2
Issue number	3
Publication status	Published - 1 Jan 2005
Externally published	Yes

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

Cite this

@article{fe590ec28f2e4d24a5ea2ae48b03aecf,

title = "L∞-Error estimates and superconvergence in maximum norm of mixed finite element methods for nonfickian flows in porous media",

abstract = "On the basis of the estimates for the regularized Green{\textquoteright}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.",

keywords = "Error estimates and superconvergence, Green{\textquoteright}s functions, Mixed finite element methods, Nonfickian flow, The mixed ritz- volterra projection",

author = "Ewing, {Richard E.} and Yanping Lin and Junping Wang and Shuhua Zhang",

year = "2005",

month = jan,

day = "1",

language = "English",

volume = "2",

pages = "301--328",

journal = "International Journal of Numerical Analysis and Modeling",

issn = "1705-5105",

publisher = "University of Alberta",

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}

L^∞-Error estimates and superconvergence in maximum norm of mixed finite element methods for nonfickian flows in porous media. / Ewing, Richard E.; Lin, Yanping; Wang, Junping et al.
In: International Journal of Numerical Analysis and Modeling, Vol. 2, No. 3, 01.01.2005, p. 301-328.

Research output: Journal article publication › Journal article › Academic research › peer-review

TY - JOUR

T1 - L∞-Error estimates and superconvergence in maximum norm of mixed finite element methods for nonfickian flows in porous media

AU - Ewing, Richard E.

AU - Lin, Yanping

AU - Wang, Junping

AU - Zhang, Shuhua

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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.

AB - 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.

KW - Error estimates and superconvergence

KW - Green’s functions

KW - Mixed finite element methods

KW - Nonfickian flow

KW - The mixed ritz- volterra projection

UR - http://www.scopus.com/inward/record.url?scp=85016218780&partnerID=8YFLogxK

M3 - Journal article

SN - 1705-5105

VL - 2

SP - 301

EP - 328

JO - International Journal of Numerical Analysis and Modeling

JF - International Journal of Numerical Analysis and Modeling

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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