Prince Chidyagwai and Beatrice Riviere, A Weak Solution and A MultiNumerics Solution of the Coupled Navier-Stokes and Darcy Equations.

This paper introduces and analyzes two models coupling the incompressible Navier-Stokes equations with the porous media flow equations. A numerical method that uses continuous finite elements in the porous medium is proposed. Existence and uniqueness results under small data condition of the numerical solution are proved. Optimal a priori error estimates are derived. Numerical results comparing the two models are provided.