Year: 2024
Author: Fan Chen, Ming Cui, Chenguang Zhou
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 201–220
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1008
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 201–220
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Nonlinear quasi-static poroelasticity problem discontinuous Galerkin method fully implicit nonlinear numerical scheme optimal convergence order estimate.