On the application of the SCD semismooth* Newton method to solving Stokes problem with stick-slip boundary conditions

V. Arzt; P. Beremlijski; H. Gfrerer; J. V. Outrata

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arXiv · 2603.29604

On the application of the SCD semismooth* Newton method to solving Stokes problem with stick-slip boundary conditions

V. Arzt·P. Beremlijski·H. Gfrerer·J. V. Outrata

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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.

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V. Arzt, P. Beremlijski, H. Gfrerer, J. V. Outrata. 2026-03-31. On the application of the SCD semismooth* Newton method to solving Stokes problem with stick-slip boundary conditions. https://arxiv.org/abs/2603.29604

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