A locking-free and mass conservative H(div) conforming DG method for the Biot's consolidation model. (15th April 2023) - He, Linshuang; Feng, Minfu; Guo, Jun
Abstract: We propose and analyze an H(div) conforming discontinuous galerkin (CDG) method for the three-field Biot's consolidation model with the displacement reconstruction technique. The displacement is discretized by the k th-order Brezzi-Douglas-Marini (BDM) element, and the fluid flux and pore pressure are approximated by the k-1 th-order Raviart-Thomas-Nedelec element pairs. The H(div) CDG method is derived from the H(div) conforming formulation by replacing the classical gradient operator with a weak gradient operator, where the weak one is locally computed by the k th-order Raviart-Thomas (RT) element. We prove optimal a-priori error estimates for both semi-discrete scheme and fully-discrete scheme with the backward Euler discretization in time. The implicit constants in the error estimates are robust for the arbitrarily large Lamé coefficient and the arbitrarily small constrained specific storage coefficient. Our method has no stabilizers, which simplifies the finite element formulations. Meanwhile, it can also overcome the poroelasticity locking mathematically and preserve the pointwise mass conservation on the discrete level. The validity and accuracy of the proposed method are verified by numerical experiments.