Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems

Abstract

This paper is devoted to a discontinuous Galerkin (DG) method for nonlinear quasi-static poroelasticity problems. The fully implicit nonlinear numerical scheme is constructed by utilizing DG method for the spatial approximation and the backward Euler method for the temporal discretization. The existence and uniqueness of the numerical solution is proved. Then we derive the optimal convergence order estimates in a discrete $H^1$ norm for the displacement and in $H^1$ and $L^2$ norms for the pressure. Finally, numerical experiments are supplied to validate the theoretical error estimates of our proposed method.