Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915234595209216 |
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| author | Stokke, Jakob S. Bause, Markus Radu, Florin A. |
| author_facet | Stokke, Jakob S. Bause, Markus Radu, Florin A. |
| contents | We study a space-time finite element method for a system of poromechanics with memory effects that are modeled by a convolution integral. In the literature, the system is referred to as the Biot-Allard model. We recast the model as a first-order system in time, where the memory effects are transformed into an auxiliary differential equation. This allows for a computationally efficient numerical scheme. The system is discretized by continuous Galerkin methods in time and equal-order finite element methods in space. An optimal order error estimate is proved for the norm of the first-order energy of the unknowns of the system. The estimate is confirmed by numerical experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system Stokke, Jakob S. Bause, Markus Radu, Florin A. Numerical Analysis We study a space-time finite element method for a system of poromechanics with memory effects that are modeled by a convolution integral. In the literature, the system is referred to as the Biot-Allard model. We recast the model as a first-order system in time, where the memory effects are transformed into an auxiliary differential equation. This allows for a computationally efficient numerical scheme. The system is discretized by continuous Galerkin methods in time and equal-order finite element methods in space. An optimal order error estimate is proved for the norm of the first-order energy of the unknowns of the system. The estimate is confirmed by numerical experiments. |
| title | Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.06763 |