(untitled) (Journal of Computational Mathematics, 2025)
In this paper, we develop a fully discrete virtual element scheme based on the local pressure projection stabilization for a three-field poroelasticity problem with a storage coefficient c_0 ≥ 0. We not only provide the well-posedness of the proposed scheme by proving a weaker form of the discrete inf-sup condition, but also show optimal error estimates for all unknowns, whose generic constants are independent of the Lamé coefficient λ. Moreover, our proposed scheme avoids pressure oscillation and applies to general polygonal elements, including hanging-node elements. Finally, we numerically validate the good performance of our virtual element scheme.