TY - JOUR
T1 - Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems
AU - Chen , Fan
AU - Cui , Ming
AU - Zhou , Chenguang
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 201
EP - 220
PY - 2024
DA - 2024/04
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1008
UR - https://global-sci.org/intro/article_detail/ijnam/23024.html
KW - Nonlinear quasi-static poroelasticity problem, discontinuous Galerkin method, fully implicit nonlinear numerical scheme, optimal convergence order estimate.
AB - <p style="text-align: justify;">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.</p>