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Volume 2, Issue 3
$L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media

R. E. Ewing, Y. Lin, J. Wang & S. Zhang

Int. J. Numer. Anal. Mod., 2 (2005), pp. 301-328.

Published online: 2005-02

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  • 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.

  • Keywords

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

  • AMS Subject Headings

76S05, 45K05, 65M12, 65M60, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-301, author = {R. E. Ewing, Y. Lin, J. Wang and S. Zhang}, title = {$L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/933.html} }
TY - JOUR T1 - $L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media AU - R. E. Ewing, Y. Lin, J. Wang & S. Zhang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 301 EP - 328 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/933.html KW - nonFickian flow, mixed finite element methods, the mixed Ritz-Volterra projection, Green's functions, error estimates and superconvergence. 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.

R. E. Ewing, Y. Lin, J. Wang and S. Zhang. (2005). $L^∞$-Error Estimates and Superconvergence in Maximum Norm of Mixed Finite Element Methods for NonFickian Flows in Porous Media. International Journal of Numerical Analysis and Modeling. 2 (3). 301-328. doi:
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