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

Author

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  • Haslinger, Jaroslav
  • Kučera, Radek
  • Motyčková, Kristina
  • Šátek, Václav

Abstract

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 (ii) 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.

Suggested Citation

  • Haslinger, Jaroslav & Kučera, Radek & Motyčková, Kristina & Šátek, Václav, 2024. "Stokes problem with the Coulomb stick–slip boundary conditions in 3D: Formulations, approximation, algorithms, and experiments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 145-167.
    • Handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:145-167
    DOI: 10.1016/j.matcom.2023.08.036
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    References listed on IDEAS

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    1. Haslinger, Jaroslav & Kučera, Radek & Sassi, Taoufik & Šátek, Václav, 2021. "Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 191-206.
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