Stokes system with local Coulomb's slip boundary conditions: Analysis of discretized models and implementation

Abstract

The theoretical part of the paper analyzes discretized Stokes systems with local Coulomb's slip boundary conditions. Solutions to discrete models are defined by means of fixed-points of an appropriate mapping. We prove the existence of a fixed-point, establish conditions guaranteeing its uniqueness and examine how they depend on the discretization parameter h and the slip coefficient kappa. The second part of the paper is devoted to computational aspects. Numerical experiments are presented.