Uniform Preconditioners For The Mixed Darcy Problem

Preconditioners for porous media flow problems in mixed form are frequently based on H(div) preconditioners rather than the pressure Schur complement. We show that when the permeability, K, is small the pressure Schur complement must also be addressed for H(div)-based preconditioners. The proposed approach is based on the operator preconditioning framework; thus, we construct the preconditioner by considering the mapping properties of the continuous operator, where the main challenge is a K-uniform inf-sup condition.