The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a mathematically rigorous {\em a posterior} error estimator which guides a greedy algorithm offline. For nonlinear and nonaffine problems, hyper reduction techniques have been introduced to make this decomposition efficient. However, they may be tricky to implement and often degrade the online computation efficiency. To avoid this degradation, reduced residual reduced over-collocation (R2-ROC) was invented integrating empirical interpolation techniques on the solution snapshots and well-chosen residuals, the collocation philosophy, and the simplicity of evaluating the hyper-reduced well-chosen residuals. In this paper, we introduce an adaptive enrichment strategy for R2-ROC rendering it capable of handling parametric fluid flow problems. Built on top of an underlying Marker and Cell (MAC) scheme, a novel hyper-reduced MAC scheme is therefore presented and tested on Stokes and Navier-Stokes equations demonstrating its high efficiency, stability and accuracy.

翻译：加速反复解决某些防腐化系统的必要性刺激了更高效的减少订单方法的开发。古典的减少基准方法由于离线分解和数学上严格的后部偏差估测器引导贪婪的离线算法而很受欢迎。对于非线性和非节食性的问题,引入了超减肥技术来提高分解效率。然而,它们可能难以实施,而且往往会降低在线计算效率。为了避免这种退化,在解决方案截图和选好残留物、合用理论以及评估高降精精精精精的残余物的简单性方面,发明了将实证性内插技术(R2-ROC)结合起来,从而在基底标记和细胞(MAC)计划顶部安装了适应性浓缩战略,从而在Stokes和Navier-Stoks方程式上展示并测试了新型的超降速计算元计算器计划,以显示其高度的稳定性和精确性。