发表机构
Politecnico di Torino（都灵理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对Navier-Stokes方程的Smagorinsky模型，采用虚拟单元框架进行数值分析，证明了解的存在唯一性，推导了二维下的先验误差收敛阶，证实无散度虚拟离散化收敛阶更高，数值结果验证了理论。
AI 中文摘要
本文在虚拟单元框架下研究Navier-Stokes方程的Smagorinsky模型，在小数据的标准假设下，证明了解的存在性与唯一性；在假设解具有更高正则性的条件下，推导了二维区域中Smagorinsky模型先验误差估计的收敛阶h；还证明了无散度虚拟离散化可提供更高的收敛阶，且所需正则性假设比有限元文献中的更弱；最后给出数值结果以验证该理论。
英文摘要
In this paper, we consider the Smagorinsky model for the Navier-Stokes equations within a virtual element framework. Under the standard assumption of small data, we prove the existence and uniqueness of a solution. Assuming more regularity to the solutions, we derive the known convergence rates $h$ for the a priori error estimates of the Smagorinsky model in two dimensional domains. We additionally prove that divergence-free virtual discretizations provide improved convergence orders, with weaker regularity assumptions than in the finite element literature. We conclude the paper with numerical results that corroborate the theory.
