A numerical method for solving the Stokes problem with a discontinuous coefficient

The Stokes problem with a piecewise constant coefficient in the elliptic operator is considered in a domain consisting of a union of two rectangles. The domain-decomposition method in combination with approximation in the subdomains by nonconforming finite elements is applied to solve this problem. The mortar finite elements are used to sew the solutions at the interface. A number of unknowns are eliminated in the resulting system of linear algebraic equations; as a result, the total number of equations become substantially lesser. An iterative method is proposed for solving the linear system obtained. Our numerical results substantiate the conclusion that such an approach can be used to solve the Stokes problem.