A Stabilized Finite Element Method for Darcy-Stokes Problems

A stabilized finite element methods for the singularly perturbed Stokes problem is proposed in this paper. This model is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson´s equation as the perturbation parameter tends to zero. The stabilized formula is uniformly stable for a traditional stable and uniformly-consistent Stokes element. The corresponding discretization error estimates are derived. Finally some 2Dnumerical experiments are carried out to verify the theoretical results.