A locking-free staggered DG method for the Biot system of poroelasticity on general polygonal meshes

Abstract

AbstractIn this paper we propose and analyze a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with a stress–displacement–rotation formulation with weak stress symmetry for arbitrary polynomial orders, which extends the piecewise constant approximation developed in Zhao and Park (2020, A staggered cell-centered DG method for linear elasticity on polygonal meshes, SIAM J. Sci. Comput.42, A2158–A2181). The proposed method is locking-free and can handle highly distorted grids, possibly including hanging nodes, which is desirable for practical applications. We prove the convergence estimates for the semidiscrete scheme and fully discrete scheme for all the variables in their natural norms. In particular, the stability and convergence analyses do not need a uniformly positive storativity coefficient. Moreover, to reduce the size of the global system, we propose a five-field-formulation-based fixed stress splitting scheme, where the linear convergence of the scheme is proved. Several numerical experiments are carried out to confirm the optimal convergence rates and the locking-free property of the proposed method.