A Priori Error Bounds for the Approximate Deconvolution Leray Reduced Order Model
<|reference_start|>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 prove a priori error bounds for the approximate deconvolution operator and 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.<|reference_end|>
@article{moore2024a,
    title={A Priori Error Bounds for the Approximate Deconvolution Leray Reduced
  Order Model},
    author={Ian Moore, Anna Sanfilippo, Francesco Ballarin, Traian Iliescu},
    journal={arXiv preprint arXiv:2410.02673},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.02673},
    primaryClass={math.NA cs.NA}
}