On the application of the SCD semismooth* Newton method to solving Stokes problem with stick-slip boundary conditions
This work addresses a specific fluid dynamics problem with stick-slip boundary conditions, representing an incremental improvement in numerical methods for this domain.
The paper tackled the 3D Stokes problem with Navier-Tresca stick-slip boundary conditions by applying a variant of the SCD semismooth* Newton method with a globalization technique, demonstrating efficiency in numerical experiments.
The paper deals with the 3D Stokes problem with Navier-Tresca stick-slip boundary conditions. A weak formulation of this problem leads to a variational inequality of the second kind, coupled with an equality constraint. This problem is then approximated using the mixed finite element method, yielding a generalized equation, to the numerical solution of which we implement a variant of the SCD semismooth* Newton method. This includes also a globalization technique ensuring convergence for arbitrary starting points. Numerical experiments demonstrate the effeciency of this approach.