Sequential symmetric interior penalty discontinuous Galerkin method for fully coupled quasi-static thermo-poroelasticity problems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912576230653952 |
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| author | Chen, Fan Cui, Ming Zhou, Chenguang |
| author_facet | Chen, Fan Cui, Ming Zhou, Chenguang |
| contents | In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin method is employed for spatial discretization and the backward Euler method for temporal discretization. Unlike other splitting algorithms, this type of sequential method does not require any internal iterations and the computational efficiency is higher than that of the fully implicit nonlinear numerical scheme. In the theoretical analysis, a cut-off operator is introduced to prove the existence and uniqueness of numerical solution and the stability analysis of numerical scheme is conducted. Then, we derive the optimal convergence order estimates in space and time. Finally, several numerical examples are presented to illustrate the accuracy and efficiency of our proposed method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_06480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequential symmetric interior penalty discontinuous Galerkin method for fully coupled quasi-static thermo-poroelasticity problems Chen, Fan Cui, Ming Zhou, Chenguang Numerical Analysis 65M15, 65M60, 76S99 In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin method is employed for spatial discretization and the backward Euler method for temporal discretization. Unlike other splitting algorithms, this type of sequential method does not require any internal iterations and the computational efficiency is higher than that of the fully implicit nonlinear numerical scheme. In the theoretical analysis, a cut-off operator is introduced to prove the existence and uniqueness of numerical solution and the stability analysis of numerical scheme is conducted. Then, we derive the optimal convergence order estimates in space and time. Finally, several numerical examples are presented to illustrate the accuracy and efficiency of our proposed method. |
| title | Sequential symmetric interior penalty discontinuous Galerkin method for fully coupled quasi-static thermo-poroelasticity problems |
| topic | Numerical Analysis 65M15, 65M60, 76S99 |
| url | https://arxiv.org/abs/2509.06480 |