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

On the convergence analysis of a hybrid numerical method for multicomponent transport in porous media