论文标题
在时间误差范围和适当正交分解的差异范围和差异的商标上
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition
论文作者
论文摘要
在本文中，我们解决了几个长期存在的问题，这些问题在时间误差范围内处理最佳的正交分解（POD）减少了热方程的订单建模。特别是，我们研究了差异商（DQS）在获得相对于时间离散误差和ROM离散误差方面最佳的差订单模型（ROM）误差界的作用。当不使用DQ时，我们证明ROM投影误差和ROM误差都是次优的。当使用DQ时，我们证明ROM投影误差和ROM误差都是最佳的。热方程的数值结果支持理论结果。
In this paper, we resolve several long standing issues dealing with optimal pointwise in time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heat equation. In particular, we study the role played by difference quotients (DQs) in obtaining reduced order model (ROM) error bounds that are optimal with respect to both the time discretization error and the ROM discretization error. When the DQs are not used, we prove that both the ROM projection error and the ROM error are suboptimal. When the DQs are used, we prove that both the ROM projection error and the ROM error are optimal. The numerical results for the heat equation support the theoretical results.
