Abstract In this paper we present an a posteriori error estimate for a reduced order model (ROM) for the incompressible Navier-Stokes equations that is based on the fact that the full order model is a finite element (FE) approximation. Both this FE approximation and the ROM are stabilized by means of a variational multi-scale (VMS) strategy, in which the unknowns are split into FE scales and sub-grid scales (SGS), the latter being modeled in terms of the former. The SGS, when properly scaled, provide directly the a posteriori error estimate, both for the ROM and for the FE approximation.

中文翻译：

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基于有限元 VMS 的不可压缩 Navier-Stokes 方程降阶模型的后验误差估计

摘要 在本文中，我们提出了不可压缩 Navier-Stokes 方程的降阶模型 (ROM) 的后验误差估计，该模型基于全阶模型是有限元 (FE) 近似这一事实。这种 FE 近似和 ROM 都通过变分多尺度 (VMS) 策略来稳定，其中未知数分为 FE 尺度和子网格尺度 (SGS)，后者根据前者建模。SGS 在适当缩放时直接为 ROM 和 FE 近似提供后验误差估计。