Sarvesh Kumar, Ricardo Oyarzúa, Ricardo Ruiz-Baier, Ruchi Sandilya:
Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity
We introduce a hybrid numerical method for the approximation of linear poroelasticity equations, representing the interaction between the non-viscous filtration flow of a fluid and the linear me- chanical 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. The resulting discrete problems exhibit a double saddle-point structure, and their solvability and stability are established in terms of bounds that do not depend on the modulus of dilation of the solid. We derive optimal error estimates in suitable norms, for all eld variables; and we exemplify the convergence and locking-free properties of this scheme through a series of numerical tests.