A Robust and Mass Conservative Virtual Element Method for Linear Three-field Poroelasticity

We present and analyze a robust and mass conservative virtual element method for the three-field formulation of Biot’s consolidation problem in poroelasticity. The displacement and fluid flux are respectively approximated by enriched H(div) virtual elements and H(div) virtual elements, while the pressure is discretized by piecewise polynomial functions. Optimal a priori error estimates are obtained, including the semi-discrete scheme and the fully-discrete scheme with the implicit Euler approximation in time. Moreover, our method achieves robustness with respect to the constants hidden in the error estimates, even for the Lamé coefficient tending to infinity and the arbitrarily small constrained specific storage coefficient, and therefore it is free of both volumetric (Poisson) locking and nonphysical pressure oscillations. Meanwhile, it also conserves pointwise mass conservation for Biot’s consolidation problem on the discrete level.