A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model

The approximate deconvolution Leray reduced order model (ADL-ROM) uses spatial filtering to increase the ROM stability, and approximate deconvolution to increase the ROM accuracy. In the under-resolved numerical simulation of convection-dominated flows, ADL-ROM was shown to be significantly more stable than the standard ROM and more accurate than the Leray ROM. In this paper, we equip ADL-ROM with a new van Cittert AD operator and prove a priori error bounds for both the AD operator and the ADL-ROM. To our knowledge, these are the first numerical analysis results for approximate deconvolution in a ROM context. We illustrate these numerical analysis results in the numerical simulation of convection-dominated flows.