On the application of the SCD semismooth* Newton method to solving Stokes problem with stick-slip boundary conditions
Numerical Analysis
2026-04-01 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2603.29604,
title = {On the application of the SCD semismooth* Newton method to solving Stokes problem with stick-slip boundary conditions},
author = {V. Arzt and P. Beremlijski and H. Gfrerer and J. V. Outrata},
journal= {arXiv preprint arXiv:2603.29604},
year = {2026}
}
Comments
30 pages, Submitted to Mathematics and Computers in Simulation