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Volume 21, Issue 2
Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems

Fan Chen, Ming Cui & Chenguang Zhou

DOI: 10.4208/ijnam2024-1008

Int. J. Numer. Anal. Mod., 21 (2024), pp. 201-220.

Published online: 2024-04

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  • 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.

  • Keywords

Nonlinear quasi-static poroelasticity problem, discontinuous Galerkin method, fully implicit nonlinear numerical scheme, optimal convergence order estimate.

  • AMS Subject Headings

65M60, 65M15, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-21-201, author = {Chen , FanCui , Ming and Zhou , Chenguang}, title = {Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1008}, url = {http://global-sci.org/intro/article_detail/ijnam/23024.html} }
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 -

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.

Chen , FanCui , Ming and Zhou , Chenguang. (2024). Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems. International Journal of Numerical Analysis and Modeling. 21 (2). 201-220. doi:10.4208/ijnam2024-1008
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