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.

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