The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes 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_ | 1866915393102151680 |
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| author | Du, Binbin Cheng, Shenxiang Yu, Yue Chen, Chuanjun |
| author_facet | Du, Binbin Cheng, Shenxiang Yu, Yue Chen, Chuanjun |
| contents | This article presents a detailed analysis of the Arrow-Hurwicz iteration applied to the solution of the incompressible Navier-Stokes equations, discretized by a divergence-free mixed virtual element method. Under a set of appropriate assumptions, it is rigorously demonstrated that the method exhibits geometric convergence, with a contraction factor that remains independent of the mesh sizes. A series of numerical experiments are conducted to validate the theoretical findings and to assess the computational performance of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations Du, Binbin Cheng, Shenxiang Yu, Yue Chen, Chuanjun Numerical Analysis Analysis of PDEs This article presents a detailed analysis of the Arrow-Hurwicz iteration applied to the solution of the incompressible Navier-Stokes equations, discretized by a divergence-free mixed virtual element method. Under a set of appropriate assumptions, it is rigorously demonstrated that the method exhibits geometric convergence, with a contraction factor that remains independent of the mesh sizes. A series of numerical experiments are conducted to validate the theoretical findings and to assess the computational performance of the proposed method. |
| title | The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2507.12036 |