Power law Stokes equations with threshold slip boundary conditions: Numerical methods and implementation

Abstract

For the power law Stokes equations driven by nonlinear slip boundary conditions of friction type, we propose three iterative schemes based on augmented Lagrangian approach and interior point method to solve the finite element approximation associated to the continuous problem. We formulate the variational problem which in this case is a variational inequality and construct the weak solution of the continuous problem. Next, we formulate two alternating direction methods based on augmented Lagrangian formalism in order to separate the velocity from the symmetric part the velocity gradient and tangential part of the velocity. Thirdly, we present some salient points of a path-following variant of the interior point method associated to the finite element approximation of the problem. Some numerical experiments are performed to confirm the validity of the schemes and allow us to compare them.