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Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D

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  • Haslinger, Jaroslav
  • Kučera, Radek
  • Sassi, Taoufik
  • Šátek, Václav

Abstract

The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity–pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:189:y:2021:i:c:p:191-206
    DOI: 10.1016/j.matcom.2020.12.015
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    References listed on IDEAS

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    1. Kučera, Radek & Haslinger, Jaroslav & Šátek, Václav & Jarošová, Marta, 2018. "Efficient methods for solving the Stokes problem with slip boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 145(C), pages 114-124.
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    Cited by:

    1. 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.
    2. Jaroslav Haslinger & Radek Kučera & Kristina Motyčková & Václav Šátek, 2021. "Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms," Mathematics, MDPI, vol. 9(22), pages 1-24, November.

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    1. Jaroslav Haslinger & Radek Kučera & Kristina Motyčková & Václav Šátek, 2021. "Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms," Mathematics, MDPI, vol. 9(22), pages 1-24, November.

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