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In this study, we consider the simulation of subsurface flow and solutetransport processes in the stationary limit. In the convection-dominant case,the numerical solution of the transport problem may exhibit non-physicaldiffusion and under- and overshoots. For an interior penalty discontinuousGalerkin (DG) discretization, we present a $h$-adaptive refinement strategyand, alternatively, a new efficient approach for reducing numerical under- andovershoots using a diffusive $L^2$-projection. Furthermore, we illustrate anefficient way of solving the linear system arising from the DG discretization.In $2$-D and $3$-D examples, we compare the DG-based methods to the streamlinediffusion approach with respect to computing time and their ability to resolvesteep fronts.

computer methods in applied mechanics and engineering

Numerical solution of steady-state groundwater flow and solute transport  problems: Discontinuous Galerkin based methods compared to the Streamline  Diffusion approach