On the Time Approximation of the Stokes Equations with Nonlinear Slip Boundary Condition

Abstract

This work is concerned with the numerical approximation of the unsteady Stokes flow of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type. The continuous problem is formulated as variational inequality, which is next discretized in time based on backward Euler's scheme. We prove existence and uniqueness of the solution of the time discrete problem by means of a regularization approach. Finally, we derive error estimates that justify the convergence property of the discretization proposed.