Year: 2019
Author: Lina Dong, Shaochun Chen
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1711-m2014-0239
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 130–150
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Darcy-Stokes problem Mixed finite elements Tetrahedral element Uniformly convergent.
Author Details
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