@Article{JCM-37-1,
author = {Lina, Dong and Shaochun, Chen},
title = {Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {1},
pages = {130--150},
abstract = {<p style="text-align: justify;">In this paper, we construct a tetrahedral element named DST20 for the three dimensional
Darcy-Stokes problem, which reduces the degrees of velocity in [30]. The finite element
space $\boldsymbol{V}_h$&nbsp;for velocity is $\boldsymbol{H}$(div)-conforming, i.e., the normal component of a function
in $\boldsymbol{V}_h$ is continuous across the element boundaries, meanwhile the tangential component
of a function in $\boldsymbol{V}_h$ is average continuous across the element boundaries, hence $\boldsymbol{V}_h$ is&nbsp;$\boldsymbol{H}^1$-average conforming. We prove that this element is uniformly convergent with respect
to the perturbation constant ε for the Darcy-Stokes problem. At the same time, we give a
discrete de Rham complex corresponding to DST20 element.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1711-m2014-0239},
url = {https://global-sci.com/article/84393/uniformly-convergent-nonconforming-tetrahedral-element-for-darcy-stokes-problem}
}