Virtual element methods for the three-field formulation of time-dependent linear poroelasticity

A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in R. Oyarzúa and R. Ruiz-Baier, (SIAM J. Numer. Anal.54 2951–2973, 2016) is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. These estimates are valid independently of the values assumed by the dilation modulus and the specific storage coefficient, implying that the formulation is locking-free. Furthermore, the accuracy of the method is verified numerically through a set of computational tests.