Fixed stress splitting approach for contact problems in a porous medium
<|reference_start|>Fixed stress splitting approach for contact problems in a porous medium: We consider a poromechanics model including frictionless contact mechanics. The resulting model consists of the Biot equations with contact boundary conditions leading to a variational inequality modelling mechanical deformations coupled to a linear parabolic flow equation. We propose a fully discrete iterative scheme for solving this model. This scheme decoupled the flow and mechanics equations and extends the fixed-stress splitting scheme for the Biot equations. We use finite elements in space and a backward Euler discretization in time. We show that the fixed stress split scheme is a contraction.<|reference_end|>
@article{almani2024fixed,
    title={Fixed stress splitting approach for contact problems in a porous medium},
    author={Tameem Almani, Kundan Kumar},
    journal={arXiv preprint arXiv:2407.13459},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13459},
    primaryClass={math.NA cs.NA}
}