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

Sarvesh Kumar, Ricardo Oyarzúa, Ricardo Ruiz-Baier, Ruchi Sandilya

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7 Citations (Scopus)


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 mixed approach is employed to approximate fluid flux and the two pressures. We focus on the stationary case and the resulting discrete problem exhibits a double saddle-point structure. Its solvability and stability are established in terms of bounds (and of norms) that do not depend on the modulus of dilation of the solid. We derive optimal error estimates in suitable norms, for all field variables; and we exemplify the convergence and locking-free properties of this scheme through a series of numerical tests.

Original languageEnglish
Pages (from-to)273-299
Number of pages27
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number1
Publication statusPublished - 1 Jan 2020
Externally publishedYes


  • Biot problem
  • Conservative schemes
  • Discontinuous finite volume methods
  • Error estimates
  • Locking-free approximations
  • Mixed finite elements

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