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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 and Shuhua Zhang
SIAM Journal on Numerical Analysis
Vol. 40, No. 4 (2003), pp. 1538-1560
Stable URL: http://www.jstor.org/stable/4101017
Page Count: 23
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Sharp L2-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media
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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 L2 superconvergence 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 L2 superconvergence 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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