Volume 9, Issue 1
An Error Estimate for MMOC-MFEM Based on Convolution for Porous Media Flow

A. Cheng ,  Y. Ren and K. Xi

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

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  • 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.

  • History

Published online: 2012-09

  • AMS Subject Headings

65N15, 65N30, 76S05

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