Splitting finite element approximations for quasi-static electroporoelasticity equations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916627296026624 |
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| author | Liu, Xuan Zou, Yongkui Zhang, Ran Cao, Yanzhao Meir, Amnon J. |
| author_facet | Liu, Xuan Zou, Yongkui Zhang, Ran Cao, Yanzhao Meir, Amnon J. |
| contents | The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on investigating its well-posedness and analyzing error estimates for a splitting backward Euler finite element method. We first define a weak solution consistent with the finite element framework. Then, we prove the uniqueness and existence of such a solution using the Galerkin method and derive a priori estimates for high-order regularity. Using a splitting technique, we define an approximate splitting solution and analyze its convergence order. Next, we apply Nedelec's curl-conforming finite elements, Lagrange elements, and the backward Euler method to construct a fully discretized scheme. We demonstrate the stability of the splitting numerical solution and provide error estimates for its convergence order in both temporal and spatial variables. Finally, we present numerical experiments to validate the theoretical results, showing that our method significantly reduces computational complexity compared to the classical finite element method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Splitting finite element approximations for quasi-static electroporoelasticity equations Liu, Xuan Zou, Yongkui Zhang, Ran Cao, Yanzhao Meir, Amnon J. Numerical Analysis Analysis of PDEs The electroporoelasticity model, which couples Maxwell's equations with Biot's equations, plays a critical role in applications such as water conservancy exploration, earthquake early warning, and various other fields. This work focuses on investigating its well-posedness and analyzing error estimates for a splitting backward Euler finite element method. We first define a weak solution consistent with the finite element framework. Then, we prove the uniqueness and existence of such a solution using the Galerkin method and derive a priori estimates for high-order regularity. Using a splitting technique, we define an approximate splitting solution and analyze its convergence order. Next, we apply Nedelec's curl-conforming finite elements, Lagrange elements, and the backward Euler method to construct a fully discretized scheme. We demonstrate the stability of the splitting numerical solution and provide error estimates for its convergence order in both temporal and spatial variables. Finally, we present numerical experiments to validate the theoretical results, showing that our method significantly reduces computational complexity compared to the classical finite element method. |
| title | Splitting finite element approximations for quasi-static electroporoelasticity equations |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2502.16811 |