  In this article, the convergence of a hybrid numerical method introduced in
Daripa and Dutta (J. Comput. Phys., 335:249-282, 2017) has been established.
This method integrates a discontinuous finite element method with a modified
method of characteristics (MMOC) in combination with finite difference (FD)
procedures, and has been successfully applied to solve a coupled system of
nonlinear equations that arises in multicomponent two-phase porous media flows.
The present convergence analysis is focused on the MMOC-FD procedure for a
nonlinear system of transport equations. For this purpose, an analogous
single-component system of transport equations has been considered and some key
ideas for possible extension to multicomponent systems have been briefly
discussed. Error estimates have been obtained and these estimates have also
been shown to be consistent with realistic numerical simulations of flows
arising in enhanced oil recovery processes.
