The role of weakly imposed Dirichlet boundary conditions for numerically stable computations of swelling phenomena

It is still a challenge to model swelling phenomena occurring in charged hydrated porous media. This is not only due to the overall complexity of the model but also to the fact that boundary conditions occur, which depend on internal variables. In the present contribution, a multi-component model based on the Theory of Porous Media (TPM) is presented. The advantage of this model is that it is thermodynamically consistent and it consists of only three primary variables. As a result of the boundary conditions depending on internal variables, the numerical treatment within the finite element method (FEM) by use of the mixed finite element scheme reveals artificial oscillations in the numerical results. To overcome these oscillations, we propose to fulfil boundary conditions weakly.