论文标题
用于不可压缩流的POD-ROM，包括全阶溶液的时间导数的快照
POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution
论文作者
论文摘要
在本文中，我们研究了通过适当的正交分解（POD）方法来处理不可压缩的Navier-Stokes方程数的速度时间导数的快照的影响。我们的一组快照包括在最初时间从完整的混合有限元法（FOM）的速度近似以及在不同时间的时间导数近似。初始速度处的近似值可以用在不同时间的速度的平均值代替，以便在实际情况下实现波动方法的方法，仅在快照集中包含时间派生词的近似值。对于POD方法，我们研究投影到$ l^2 $和$ h^1 $之间的差异。在这两种情况下，在时间错误范围内都可以证明。在FOM和POD方法中都可以在粘度的反向逆力下进行误差界定。
In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods. Our set of snapshots includes the velocity approximation at the initial time from a full order mixed finite element method (FOM) together with approximations to the time derivative at different times. The approximation at the initial velocity can be replaced by the mean value of the velocities at the different times so that implementing the method to the fluctuations, as done mostly in practice, only approximations to the time derivatives are included in the set of snapshots. For the POD method we study the differences between projecting onto $L^2$ and $H^1$. In both cases pointwise in time error bounds can be proved. Including grad-div stabilization both in the FOM and POD methods error bounds with constants independent on inverse powers of the viscosity can be obtained.
