Discontinous Galerkin Methods for Coupled Flow and Transport problems

We investigate the use of discontinuous Galerkin finite element methods in a mul- tiphysics setting involving coupled flow and transport in porous media. We solve an elliptic equation for the fluid pressure using Nitsche’s method and an approxima- tion, Σ, of the exact convection field σ will be constructed by interpolation onto the lowest-order Raviart-Thomas space of functions. We sequentially solve the transport equation, with the convection field Σ, for the fluid saturation by use of the lowest order discontinuous Galerkin method. We also supply numerical evidence of the importance of local conservation in this setting, and furthermore propose a line of argument indicating that if Σ is constructed using conservative fluxes, the modeling error σ − Σ may not have a great impact on the total error in certain quantities of interest.