Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914293933408256 |
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| author | Zhang, Jiachuan |
| author_facet | Zhang, Jiachuan |
| contents | This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a priori error estimates that clearly distinguish the pressure dependence of the two discretizations: the velocity error of the classical scheme depends on both the exact pressure and the viscosity, whereas the pressure-robust method eliminates both entirely. Moreover, we derive pressure error estimates and quantify their dependence on the exact solution and model parameters. Two-dimensional numerical experiments validate the theoretical findings, including higher-order tests up to polynomial degree three and a lid-driven cavity benchmark with a piecewise linear interface. The implementation code is made publicly available to facilitate reproducibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem Zhang, Jiachuan Numerical Analysis This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a priori error estimates that clearly distinguish the pressure dependence of the two discretizations: the velocity error of the classical scheme depends on both the exact pressure and the viscosity, whereas the pressure-robust method eliminates both entirely. Moreover, we derive pressure error estimates and quantify their dependence on the exact solution and model parameters. Two-dimensional numerical experiments validate the theoretical findings, including higher-order tests up to polynomial degree three and a lid-driven cavity benchmark with a piecewise linear interface. The implementation code is made publicly available to facilitate reproducibility. |
| title | Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.19116 |