Low Order Nonconforming Rectangular Finite Element Methods for Darcy-Stokes Problems (Journal of Computational Mathematics, 2018)
In this paper, we consider lower order rectangular finite element methods for the singularlyperturbed Stokes problem. The model problem reduces to a linear Stokes problemwhen the perturbation parameter is large and degenerates to a mixed formulation of Poisson'sequation as the perturbation parameter tends to zero. We propose two 2D andtwo 3D nonconforming rectangular finite elements, and derive robust discretization errorestimates. Numerical experiments are carried out to verify the theoretical results.
Keywords: Darcy-Stokes problem; Finite element; Uniformly stable.