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

A. Cheng, Y. Ren & K. Xi

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

Published online: 2012-09

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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.

  • Keywords

Porous medium flow, characteristic methods, Bramble-Schatz kernel, convolution, convergence analysis.

  • AMS Subject Headings

65N15, 65N30, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-149, author = {}, title = {An Error Estimate for MMOC-MFEM Based on Convolution for Porous Media Flow}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {1}, pages = {149--168}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/617.html} }
TY - JOUR T1 - An Error Estimate for MMOC-MFEM Based on Convolution for Porous Media Flow JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 149 EP - 168 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/617.html KW - Porous medium flow, characteristic methods, Bramble-Schatz kernel, convolution, convergence analysis. AB -

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.

A. Cheng, Y. Ren & K. Xi. (1970). An Error Estimate for MMOC-MFEM Based on Convolution for Porous Media Flow. International Journal of Numerical Analysis and Modeling. 9 (1). 149-168. doi:
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