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.