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

Jaroslav Haslinger, Radek Kučera, Kristina Motyčková and Václav Šátek

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 216, issue C, 145-167

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.

Keywords: Stokes problem; Coulomb stick–slip boundary conditions; Successive approximations; Semi-smooth Newton method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:216:y:2024:i:c:p:145-167

DOI: 10.1016/j.matcom.2023.08.036

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