An Error Estimate for MMOC-MFEM Based on Convolution for Porous Media Flow
Keywords:
Porous medium flow, characteristic methods, Bramble-Schatz kernel, convolution, convergence analysis.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.