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Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations

Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations
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Year:    2016

Author:    Gang Chen, Minfu Feng, Xiaoping Xie

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1604-m2015-0447

Journal of Computational Mathematics, Vol. 34 (2016), Iss. 5 : pp. 549–572

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

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

Author Details

Gang Chen

Minfu Feng

Xiaoping Xie

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