Abstract In this paper, we propose and investigate a divergence-free reconstruction of the nonconforming virtual element for the Stokes problem. By constructing the computable Raviart–Thomas-like interpolation operator, we guarantee the independence between the velocity error estimation | u − u h | 1 , h and the continuous pressure p , as it happens for the divergence-free flow solver. Moreover, this modified scheme can also inherit the advantages of the classical nonconforming virtual element method, such as, very general meshes including non-convex and degenerate elements, a unified scheme for an arbitrary-order approximation accuracy k , etc. Then, we provide the optimal L 2 -error estimates for the velocity gradient and the pressure by taking advantage of the Raviart–Thomas-like interpolation operator and avoiding the use of a trace inequality. Finally, three numerical experiments are presented to conform the theoretical analysis.

中文翻译：

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斯托克斯问题非一致虚元法的无散度重构

摘要 在本文中，我们提出并研究了斯托克斯问题的非一致性虚拟元素的无散度重建。通过构造可计算的 Raviart-Thomas-like 插值算子，我们保证了速度误差估计和速度误差估计之间的独立性。你 - 呃 | 1 、 h 和连续压力 p ，就像无发散流动求解器一样。此外，这种修改后的方案还可以继承经典的非一致虚元方法的优点，例如非常通用的网格包括非凸和退化单元，任意阶近似精度 k 的统一方案等。 然后，我们提供通过利用 Raviart-Thomas-like 插值算子并避免使用迹不等式，对速度梯度和压力的最佳 L 2 误差估计。