发表机构
Hong Kong Baptist University（香港浸会大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种用于不可压缩Navier--Stokes方程的二阶指数低正则性积分器，仅需线性求解，满足离散能量衰减，在$H^4$有界条件下达到二阶时间收敛，并扩展至有限元方法。
AI 中文摘要
针对不可压缩Navier--Stokes方程，提出了一种二阶指数低正则性积分器。该方法仅需线性求解，并满足离散能量衰减性质。在均匀$H^4$解有界条件下，建立了二阶时间收敛性，且误差常数在黏性趋于零时保持有界。对于Fourier--Galerkin离散化，在固定黏性下建立了最优空间收敛率。该方法还可扩展到协调有限元方法，同时保留离散能量衰减结构。数值结果证实了收敛阶数以及对黏性的鲁棒性。
英文摘要
A second-order exponential low-regularity integrator is proposed for the incompressible Navier--Stokes equations. The method requires only linear solves and satisfies a discrete energy-decay property. Second-order temporal convergence is established under a uniform $H^4$ solution bound, with an error constant that remains bounded as the viscosity tends to zero. For the Fourier--Galerkin discretization, the optimal spatial convergence rate is established for fixed viscosity. The method can also be extended to conforming finite element methods while retaining the discrete energy-decay structure. Numerical results confirm the convergence orders and robustness with respect to the viscosity.
