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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.

Gang Chen, Minfu Feng & Xiaoping Xie. (2019). 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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