A coupled model of the fluid flow with nonlinear slip Tresca boundary condition

Abstract

In this article, we consider the finite element discretization of the time-dependent Stokes equations written under the Boussinesq approximation, coupled with the convection-diffusion equation and provided with Tresca's Friction Law. Existence and uniqueness of a solution are established. To solve Stokes variational inequality, we suggest an alternating direction method of multiplier. We derive some a priori estimates and validate the obtained theoretical results by numerical simulations.