TY - JOUR
T1 - An Error Estimate for MMOC-MFEM Based on Convolution for Porous Media Flow
AU - A. Cheng, Y. Ren & K. Xi
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 - <p style="text-align: justify;">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.</p>