@Article{IJNAM-20-3,
author = {Kiera, Kean and Xihui, Xie and Xu, Shuxian},
title = {A Doubly Adaptive Penalty Method for the Navier Stokes Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {3},
pages = {407--436},
abstract = {<p style="text-align: justify;">We develop, analyze and test adaptive penalty parameter methods. We prove unconditional stability for velocity when adapting the penalty parameter, $ϵ,$ and stability of the velocity
time derivative under a condition on the change of the penalty parameter, $ϵ(t_{n+1}) − ϵ(t_n).$ The
analysis and tests show that adapting $ϵ(t_{n+1})$ in response to $∇·u(t_n)$ removes the problem of
picking $ϵ$ and yields good approximations for the velocity. We provide error analysis and numerical
tests to support these results. We supplement the adaptive-$ϵ$ method by also adapting the time-step. The penalty parameter ϵ and time-step are adapted independently. We further compare
first, second and variable order time-step algorithms. Accurate recovery of pressure remains an
open problem.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2023-1017},
url = {https://global-sci.com/article/82899/a-doubly-adaptive-penalty-method-for-the-navier-stokes-equations}
}