Hybridizable Discontinuous Galerkin Methods for Thermo-Poroelastic Systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913906734137344 |
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| author | Meddahi, Salim |
| author_facet | Meddahi, Salim |
| contents | We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and fluid velocities, heat flux, effective stress, pore pressure, and temperature as state variables. We establish well-posedness of the continuous problem using semigroup theory and develop an energy-consistent HDG discretization. The method exploits computational advantages of HDG-including locality and static condensation-while maintaining energy conservation for the coupled system. We establish an $hp$-convergence analysis and support it with comprehensive numerical experiments, confirming the theoretical rates and showcasing the method's effectiveness for thermo-poroelastic wave propagation in heterogeneous media. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hybridizable Discontinuous Galerkin Methods for Thermo-Poroelastic Systems Meddahi, Salim Numerical Analysis We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and fluid velocities, heat flux, effective stress, pore pressure, and temperature as state variables. We establish well-posedness of the continuous problem using semigroup theory and develop an energy-consistent HDG discretization. The method exploits computational advantages of HDG-including locality and static condensation-while maintaining energy conservation for the coupled system. We establish an $hp$-convergence analysis and support it with comprehensive numerical experiments, confirming the theoretical rates and showcasing the method's effectiveness for thermo-poroelastic wave propagation in heterogeneous media. |
| title | Hybridizable Discontinuous Galerkin Methods for Thermo-Poroelastic Systems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.17978 |