论文标题
部分可观测时空混沌系统的无模型预测
Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data
论文作者
论文摘要
在本文中，分析了半分化和完全离散的有限元方法，用于使用非平滑初始数据的受惩罚的二维不稳定的Navier-Stokes方程。一阶向后欧拉方法用于时间离散化，而符合有限元方法则用于空间离散化。对于数据的最佳$ l^2 $错误估计以及速度和压力的完全离散近似值是针对数据上实际假定的条件得出的。证明中的主要成分是对受罚的Stokes操作员的倒数，负标准估计和时间加权估计值的适当开采。最后讨论了数值示例，该示例符合我们的理论结果。
In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the time discretization, whereas conforming finite element method is used for the spatial discretization. Optimal $L^2$ error estimates for the semidiscrete as well as the fully discrete approximations of the velocity and of the pressure are derived for realistically assumed conditions on the data. The main ingredient in the proof is the appropriate exploitation of the inverse of the penalized Stokes operator, negative norm estimates and time weighted estimates. Numerical examples are discussed at the end which conform our theoretical results.
