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

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

@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://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/617.html KW - Porous medium flow KW - characteristic methods KW - Bramble-Schatz kernel KW - convolution KW - 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.