Stokes problem with the Coulomb stick-slip boundary conditions in 3D: Formulations, approximation, algorithms, and experiments

The paper deals with the approximation and numerical realization of the Stokes system in 3D with Coulomb's slip boundary conditions. The weak velocity-pressure formulation leads to an implicit inequality type problem which is discretized by the P1+bubble/P1 elements. To regularize the discrete non-smooth slip term and to release the discrete impermeability condition the duality approach is used. For numerical realization of the resulting saddle-point problem two strategies are proposed, namely (i) its fixed-point formulation solved by the method of successive approximations (i i) the direct numerical solution of the saddle-point problem. The semi-smooth Newton method is used to solve non-smooth equations appearing in both these approaches. (c) 2023 The Authors. Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper focuses on the approximation and numerical realization of the three-dimensional Stokes system with Coulomb's slip boundary conditions. By using the P1+bubble/P1 elements to discretize the weak velocity-pressure formulation, the discrete non-smooth slip term and impermeability condition are effectively addressed. The duality approach and the semi-smooth Newton method are proposed as strategies for solving the resulting saddle-point problem.