Error analysis of the semi-discrete local discontinuous Galerkin method for compressible miscible displacement problem in porous media

In this paper, local discontinuous Galerkin method for flow and transport is introduced for the coupled system of compressible miscible displacement problem. Optimal error estimates in L∞(0,T;L2)L∞(0,T;L2) norm not only for the solution itself but also for the auxiliary variables are derived. The main technical difficulties in the analysis include the nonlinearity, the coupling of the models and the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method. The numerical results illustrate the accuracy and capability of the method.