@Article{NMTMA-1-3,
author = {},
title = {A $\mathbb{P}_N × \mathbb{P}_N$ Spectral Element Projection Method for the Unsteady Incompressible Navier-Stokes Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2008},
volume = {1},
number = {3},
pages = {275--296},
abstract = {<p style="text-align: justify;">In this paper, we present a $\mathbb{P}_N × \mathbb{P}_N$ spectral element method and a detailed
comparison with existing methods for the unsteady incompressible Navier-Stokes equations.
The main purpose of this work consists of: (i) detailed comparison and discussion
of some recent developments of the temporal discretizations in the frame of spectral element
approaches in space; (ii) construction of a stable $\mathbb{P}_N × \mathbb{P}_N$ method together with
a $\mathbb{P}_N → \mathbb{P}_{N-2}$&nbsp;post-filtering. The link of different methods will be clarified. The key
feature of our method lies in that only one grid is needed for both velocity and pressure
variables, which differs from most well-known solvers for the Navier-Stokes equations.
Although not yet proven by rigorous theoretical analysis, the stability and accuracy of
this one-grid spectral method are demonstrated by a series of numerical experiments.</p>},
issn = {2079-7338},
doi = {https://doi.org/2008-NMTMA-6052},
url = {https://global-sci.com/article/90782/a-mathbbp-n-mathbbp-n-spectral-element-projection-method-for-the-unsteady-incompressible-navier-stokes-equations}
}