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

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 in- equality 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 solu- tion of the saddle-point problem. The semi-smooth Newton method is used to solve non-smooth equations appearing in both these approaches.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 in- equality 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 solu- tion of the saddle-point problem. The semi-smooth Newton method is used to solve non-smooth equations appearing in both these approaches.