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Int. J. Numer. Anal. Mod., 2 (2005), pp. 301-328. |
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L^infty-error estimates and superconvergence in maximum norm of mixed finite element methods for NonFickian flows in porous media Richard E. Ewing 1, Yanping Lin 2, Junping Wang 3, Shuhua Zhang 4 1 Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3404, USA2 Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 Canada 3 Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401, USA 4 Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, and Liu Hui Center for Applied Mathematics, Nankai University and Tianjin University, China Received by the editors January 1, 2004 and, in revised form, June 22, 2004 Abstract On the basis of the estimates for the regularized Green's functions with memory terms, optimal order L-infinity-error estimates are established for the nonFickian flow of fluid in porous media by means of a mixed Ritz-Volterra projection. Moreover, local L-infinity-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-infinity-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. AMS subject classifications: 76S05, 45K05, 65M12, 65M60, 65R20 Key words: nonFickian flow; mixed finite element methods; the mixed Ritz-Volterra projection; Green's functions; error estimates and superconvergence Email: ewing@isc.tamu.edu (R. E. Ewing), ylin@math.ualberta.ca (Y. Lin), jwang@mines.edu (J. Wang), shuhua@eyou.com (S. Zhang) |