Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem

Uniformly Convergent Nonconforming Tetrahedral Element for Darcy-Stokes Problem

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

Lina Dong

Shaochun Chen