TY - JOUR
T1 - Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem
AU - Dong , Lina
AU - Chen , Shaochun
JO - Journal of Computational Mathematics
VL - 1
SP - 130
EP - 150
PY - 2018
DA - 2018/08
SN - 37
DO - http://doi.org/10.4208/jcm.1711-m2014-0239
UR - https://global-sci.org/intro/article_detail/jcm/12653.html
KW - Darcy-Stokes problem, Mixed finite elements, Tetrahedral element, Uniformly
convergent.
AB - <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>