Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity

@article{Kumar2020ConservativeDF,
  title={Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity},
  author={Sarvesh Kumar and Ricardo Oyarz{\'u}a and Ricardo Ruiz Baier and Ruchi Sandilya},
  journal={Mathematical Modelling and Numerical Analysis},
  year={2020},
  volume={54},
  pages={273-299}
}
We introduce a numerical method for the approximation of linear poroelasticity equations, representing the interaction between the non-viscous filtration flow of a fluid and the linear mechanical response of a porous medium. In the proposed formulation, the primary variables in the system are the solid displacement, the fluid pressure, the fluid flux, and the total pressure. A discontinuous finite volume method is designed for the approximation of solid displacement using a dual mesh, whereas a… 
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