$L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media

$L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media

Year:    2005

International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 3 : pp. 301–328

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2005-IJNAM-933

International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 3 : pp. 301–328

Published online:    2005-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    nonFickian flow mixed finite element methods the mixed Ritz-Volterra projection Green's functions error estimates and superconvergence.