@Article{JCM-26-3,
author = {},
title = {Finite Element Methods for the Navier-Stokes Equations by $H(div)$ Elements},
journal = {Journal of Computational Mathematics},
year = {2008},
volume = {26},
number = {3},
pages = {410--436},
abstract = {<p style="text-align: justify;">We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using $H(div)$ conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the $H(div)$ finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.</p>},
issn = {1991-7139},
doi = {https://doi.org/2008-JCM-10360},
url = {https://global-sci.com/article/84940/finite-element-methods-for-the-navier-stokes-equations-by-hdiv-elements}
}