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Volume 34, Issue 5
Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations

Gang Chen, Minfu Feng & Xiaoping Xie

DOI: 10.4208/jcm.1604-m2015-0447

J. Comp. Math., 34 (2016), pp. 549-572.

Published online: 2016-10

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  • Abstract

This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the $P_k/P_{k-1} (k ≥ 1)$ discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise $P_l/P_k (l=k-1,k)$ for the trace approximations of the velocity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods.

  • Keywords

Stokes equations, Weak Galerkin, Globally divergence-free, Uniform error estimates, Local elimination.

  • AMS Subject Headings

65M60, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

569615491@qq.com (Gang Chen)

fmf@wtjs.cn (Minfu Feng)

xpxie@scu.edu.cn (Xiaoping Xie)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-549, author = {Chen , GangFeng , Minfu and Xie , Xiaoping}, title = {Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {5}, pages = {549--572}, abstract = {

This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the $P_k/P_{k-1} (k ≥ 1)$ discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise $P_l/P_k (l=k-1,k)$ for the trace approximations of the velocity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1604-m2015-0447}, url = {http://global-sci.org/intro/article_detail/jcm/9812.html} }
TY - JOUR T1 - Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations AU - Chen , Gang AU - Feng , Minfu AU - Xie , Xiaoping JO - Journal of Computational Mathematics VL - 5 SP - 549 EP - 572 PY - 2016 DA - 2016/10 SN - 34 DO - http://doi.org/10.4208/jcm.1604-m2015-0447 UR - https://global-sci.org/intro/article_detail/jcm/9812.html KW - Stokes equations, Weak Galerkin, Globally divergence-free, Uniform error estimates, Local elimination. AB -

This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the $P_k/P_{k-1} (k ≥ 1)$ discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise $P_l/P_k (l=k-1,k)$ for the trace approximations of the velocity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods.

Chen , GangFeng , Minfu and Xie , Xiaoping. (2016). Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations. Journal of Computational Mathematics. 34 (5). 549-572. doi:10.4208/jcm.1604-m2015-0447
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