@Article{CiCP-19-1409,
author = {Qilong Zhai, Ran Zhang and Lin Mu},
title = {A New Weak Galerkin Finite Element Scheme for the Brinkman Model},
journal = {Communications in Computational Physics},
year = {2018},
volume = {19},
number = {5},
pages = {1409--1434},
abstract = {<p style="text-align: justify;">The Brinkman model describes flow of fluid in complex porous media with
a high-contrast permeability coefficient such that the flow is dominated by Darcy in
some regions and by Stokes in others. A weak Galerkin (WG) finite element method
for solving the Brinkman equations in two or three dimensional spaces by using polynomials
is developed and analyzed. The WG method is designed by using the generalized
functions and their weak derivatives which are defined as generalized distributions.
The variational form we considered in this paper is based on two gradient operators
which is different from the usual gradient-divergence operators for Brinkman
equations. The WG method is highly flexible by allowing the use of discontinuous
functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-order
error estimates are established for the corresponding WG finite element solutions
in various norms. Some computational results are presented to demonstrate the
robustness, reliability, accuracy, and flexibility of the WG method for the Brinkman
equations.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.scpde14.44s},
url = {http://global-sci.org/intro/article_detail/cicp/11136.html}
}