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Volume 37, Issue 1
Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem

Lina Dong & Shaochun Chen

DOI: 10.4208/jcm.1711-m2014-0239

J. Comp. Math., 37 (2019), pp. 130-150.

Published online: 2018-08

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  • Abstract

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 $\boldsymbol{V}_h$ 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 $\boldsymbol{H}^1$-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.

  • Keywords

Darcy-Stokes problem, Mixed finite elements, Tetrahedral element, Uniformly convergent.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

dln3515@163.com (Lina Dong)

shchchen@zzu.edu.cn (Shaochun Chen)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-130, author = {Dong , Lina and Chen , Shaochun}, title = {Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {1}, pages = {130--150}, abstract = {

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 $\boldsymbol{V}_h$ 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 $\boldsymbol{H}^1$-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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1711-m2014-0239}, url = {http://global-sci.org/intro/article_detail/jcm/12653.html} }
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 -

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 $\boldsymbol{V}_h$ 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 $\boldsymbol{H}^1$-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.

Dong , Lina and Chen , Shaochun. (2018). Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem. Journal of Computational Mathematics. 37 (1). 130-150. doi:10.4208/jcm.1711-m2014-0239
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