An $hp$ Error Analysis of HDG for Dynamic Poroelasticity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929753326354432 |
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| author | Meddahi, Salim |
| author_facet | Meddahi, Salim |
| contents | This study introduces a hybridizable discontinuous Galerkin (HDG) method for simulating low-frequency wave propagation in poroelastic media. We present a novel four-field variational formulation and establish its well-posedness and energy stability. Our \(hp\)-convergence analysis of the HDG method for spatial discretization is complemented by a Crank-Nicolson scheme for temporal discretization. Numerical experiments validate the theoretical convergence rates and demonstrate the effectiveness of the method in accurately capturing poroelastic dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An $hp$ Error Analysis of HDG for Dynamic Poroelasticity Meddahi, Salim Numerical Analysis 65N12, 65N15, 65N30 This study introduces a hybridizable discontinuous Galerkin (HDG) method for simulating low-frequency wave propagation in poroelastic media. We present a novel four-field variational formulation and establish its well-posedness and energy stability. Our \(hp\)-convergence analysis of the HDG method for spatial discretization is complemented by a Crank-Nicolson scheme for temporal discretization. Numerical experiments validate the theoretical convergence rates and demonstrate the effectiveness of the method in accurately capturing poroelastic dynamics. |
| title | An $hp$ Error Analysis of HDG for Dynamic Poroelasticity |
| topic | Numerical Analysis 65N12, 65N15, 65N30 |
| url | https://arxiv.org/abs/2503.08360 |