Nonconforming Finite Element Analysis Of Darcy-Stokes Problem

In this paper,we study the nonconforming finite element method of singularly perturbed Darcy-Stokes problem.Firstly,we analyze the existence and uniqueness of the solutions of the singular perturbation Darcy-Stokes equations,and then analyze the conditions that the convergence of the discrete problem should be satisfied.We construct a new nonconforming triangular element,two rectangular elements,which are convergent to the singular perturbation Darcy-Stokes equations.Two order convergent results for velocity and pressure are obtained.Finally,we present some numerical experiments verifying the theoretical analysis results.