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A weak Galerkin finite element method for the coupled Stokess-Biot problem

  • Rui Li
  • Hui Peng
  • Xiuli Wang
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Abstract

In this paper,we consider a stable numerical method for the Stokes-Biot model. We adopt the standard formulation of the Stokes equations coupled with the mixed formulation of the Biot system involving the additional total pressure variable. We construct the semi-discrete scheme on polygonal meshes by employing weak Galerkin finite element methods for spatial discretization. It is convenient to incorporate the interface conditions into the semi-discrete scheme via the edge-based degrees of freedom. Furthermore, we give a fully discrete scheme based on the backward Euler method. We establish the well-posedness of these two schemes and provide a rigorous error analysis. Finally, we present some numerical examples to verify the convergence and stability of our algorithm under a wide range of some physical parameters.

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Cite

BibTeXRIS
BibTeX
@misc{li2026weak,
  title = {{A weak Galerkin finite element method for the coupled Stokess-Biot problem}},
  author = {Rui Li and Hui Peng and Xiuli Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06335},
  eprint = {2611.06335},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06335},
}
RIS
TY  - UNPB
TI  - A weak Galerkin finite element method for the coupled Stokess-Biot problem
AU  - Rui Li
AU  - Hui Peng
AU  - Xiuli Wang
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06335
UR  - https://arxiv.org/abs/2611.06335
AB  - In this paper,we consider a stable numerical method for the Stokes-Biot model. We adopt the standard formulation of the Stokes equations coupled with the mixed formulation of the Biot system involving the additional total pressure variable. We construct the semi-discrete scheme on polygonal meshes by employing weak Galerkin finite element methods for spatial discretization. It is convenient to incorporate the interface conditions into the semi-discrete scheme via the edge-based degrees of freedom. Furthermore, we give a fully discrete scheme based on the backward Euler method. We establish the well-posedness of these two schemes and provide a rigorous error analysis. Finally, we present some numerical examples to verify the convergence and stability of our algorithm under a wide range of some physical parameters.
ER  -