A stabilized mixed discontinuous Galerkin method for Darcy flow

A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two- and three-dimensional constant-flow “patch tests” for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters.