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

ABSTRACT 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.