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arXiv · 2507.12036

The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations

Binbin Du·Shenxiang Cheng·Yue Yu·Chuanjun Chen
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Abstract

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.

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Binbin Du, Shenxiang Cheng, Yue Yu, Chuanjun Chen. 2025-07-16. The Arrow-Hurwicz iteration for virtual element discretizations of the incompressible Navier-Stokes equations. https://arxiv.org/abs/2507.12036

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