A virtual element method for overcoming locking phenomena in Biot's consolidation model

Abstract

A novel algorithm for the three-field formulation of Biot's consolidation model based on mixed and divergence-free nonconforming virtual element methods is developed and analyzed. By establishing a discrete counterpart of Korn's inequality, we ensure the well-posedness of this algorithm without special constraints in the context of nonconforming methods. In addition, we also derive a unified error estimate for this fully discrete algorithm no matter whether the specific storage coefficient vanishes or not. Moreover, this algorithm has several features, including supporting general polygonal meshes and arbitrary space approximation orders, and without Poisson's locking and pressure oscillations. Numerical experiments are presented to validate the performance of this algorithm.