Long-time error estimate and decay of finite element method to a generalized viscoelastic flow
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911027568836608 |
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| author | Guo, Yingwen He, Yinnian Qiu, Wenlin Zheng, Xiangcheng |
| author_facet | Guo, Yingwen He, Yinnian Qiu, Wenlin Zheng, Xiangcheng |
| contents | This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power-law memory kernel. We prove regularity and long-time exponential decay of the solutions, as well as a long-time convolution-type Grönwall inequality to support numerical analysis. A Volterra-Stokes projection is developed and analyzed to facilitate the parabolic-type duality argument, leading to the long-time error estimates and exponential decay of velocity and pressure. A benchmark problem of planar four-to-one contraction flow is simulated to substantiate the generality of the proposed model in comparison with the Navier-Stokes equation and Oldroyd's model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22782 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time error estimate and decay of finite element method to a generalized viscoelastic flow Guo, Yingwen He, Yinnian Qiu, Wenlin Zheng, Xiangcheng Numerical Analysis This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power-law memory kernel. We prove regularity and long-time exponential decay of the solutions, as well as a long-time convolution-type Grönwall inequality to support numerical analysis. A Volterra-Stokes projection is developed and analyzed to facilitate the parabolic-type duality argument, leading to the long-time error estimates and exponential decay of velocity and pressure. A benchmark problem of planar four-to-one contraction flow is simulated to substantiate the generality of the proposed model in comparison with the Navier-Stokes equation and Oldroyd's model. |
| title | Long-time error estimate and decay of finite element method to a generalized viscoelastic flow |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.22782 |