Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations

Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in the L² norm. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017