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<p>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 virtual element method. Under a set of appropriate assumptions, it is rigorously demonstrated that the method exhibits geometric convergence, with a parameter 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.</p>

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The Arrow-Hurwicz Iteration for Virtual Element Discretizations of the Incompressible Navier-Stokes Equations

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Binbin Du,
  • Shenxiang Cheng,
  • Yue Yu,
  • Chuanjun Chen

摘要

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 virtual element method. Under a set of appropriate assumptions, it is rigorously demonstrated that the method exhibits geometric convergence, with a parameter 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.