Coupled generalized non-linear stokes flow with flow through a porous medium
byV. J. Ervin, E. W. Jenkins, S. Sun
V. J. Ervin, E. W. Jenkins, and S. Sun, “Coupled generalized non-linear stokes flow with flow through a porous medium”, SIAM Journal on Numerical Analysis, 47(2), 929–952, 2009.
In this article, we analyze the flow of a fluid through a coupled Stokes–Darcy domain. The fluid in each domain is non-Newtonian, modeled by the generalized nonlinear Stokes equation in the free flow region and the generalized nonlinear Darcy equation in the porous medium. A flow rate is specified along the inflow portion of the free flow boundary. We show existence and uniqueness of a variational solution to the problem. We propose and analyze an approximation algorithm and establish a priori error estimates for the approximation.