Local post-processing for locally conservative fluxes in the Galerkin method for groundwater flows

The Galerkin Finite-Element Method using bilinear basis functions (in two dimensions) offers many advantages in the numerical treatment of flow through porous media. A significant disadvantage of this approach, however, is the lack of an explicit discrete requirement of conservation of mass on mesh cells. While this shortcoming is a concern in the case of single-phase flows, it is critical in the case of multi-phase flows, where lack of conservation may lead to inaccurate or non-physical simulations. Here, we extend the approach of Cordes and Kinzelbach [1992] for computing continuous velocity fields based on finite-element solution data to the important cases of heterogeneous media, non-zero recharge, and non-homogeneous boundary conditions. We introduce a new technique, which solves a problem similar to that in Cordes and Kinzelbach [1992], but using a local mixed finite element basis. Finally, we compare the two approaches and give numerical results that demonstrate the usefulness of the improved velocity fields.