Int. J. Numer. Anal. Mod., 9 (2012), pp. 149-168.


An error estimate for MMOC-MFEM based on convolution for porous media flow

A. Cheng, Y. Ren and K. Xi 1, Y. Ren 1, K. Xi 1

1 School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received by the editors August 16, 2009 and, in revised form, December 26, 2009.
Abstract

A modification of the modified method of characteristics (MMOC) is introduced for solving the coupled system of partial differential equations governing miscible displacement in porous media . The pressure-velocity is approximated by a mixed finite element procedure using a Raviart-Thomas space of index k over a uniform grid. The resulting Darcy velocity is post-processed by convolution with Bramble-Schatz kernel and this enhanced velocity is used in the evaluation of the coefficients in MMOC for the concentration equation. If the concentration space is of local degree l, then, the error in the concentration is $O(h^{l+1}_c+h^{2k+2}_p)$, which reflects the superconvergence of velocity approximation.

AMS subject classifications: 65N15, 65N30, 76S05
Key words: Porous medium flow, characteristic methods, Bramble-Schatz kernel, convolution, convergence analysis.
 

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