Stabilized methods and post-processing techniques for miscible displacements

Stabilized finite element formulations and post-processing techniques are presented for Darcy flow and miscible displacement problems. In these techniques all primary unknowns are approximated in space by standard equal-order interpolations. We presented a review of the main mathematical results, including convergence estimates for global post-processing to solve the pressure-velocity problem and for the stabilized solution of the complete set of coupled partial differential equations in both space-time and semi-discrete frameworks. Demonstration problems are solved to show that we obtained numerically high rates of convergence than those predicted, achieving good accuracy in the solution of monophasic flow problems in adverse conditions. (C) 2004 Elsevier B.V. All rights reserved.