TY - JOUR
T1 - A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model
AU - Wang , Xiuli
AU - Zhai , Qilong
AU - Wang , Xiaoshen
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 360
EP - 380
PY - 2019
DA - 2019/01
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0115
UR - https://global-sci.org/intro/article_detail/aamm/12967.html
KW - Incompressible Stokes equation, weak Galerkin finite element method, discrete weak gradient, Schur complement.
AB - <p style="text-align: justify;">In this paper, we propose a weak Galerkin finite element method (WG) for solving the stationary incompressible Stokes equation in two or three dimensional space. The weak Galerkin finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. However, since additional variables are introduced, the computational cost is much higher. Our new method can significantly reduce the computational cost&nbsp; while maintaining the accuracy. Optimal error orders are established for the weak Galerkin finite element approximations in various norms. Some numerical results are presented to demonstrate the efficiency of the method.</p>