TY - JOUR
T1 - Nonconforming Finite Element Method Applied to the Driven Cavity Problem
AU - Roktaek Lim & Dongwoo Sheen
JO - Communications in Computational Physics
VL - 4
SP - 1012
EP - 1038
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.OA-2016-0039
UR - https://global-sci.org/intro/article_detail/cicp/11269.html
KW - 
AB - <p style="text-align: justify;">A cheapest stable nonconforming finite element method is presented for
solving the incompressible flow in a square cavity without smoothing the corner singularities.
The stable cheapest nonconforming finite element pair based on P<sub>1</sub>×P<sub>0</sub> on
rectangular meshes [29] is employed with a minimal modification of the discontinuous
Dirichlet data on the top boundary, where $\widetilde{\mathcal{P}^h_0}$&nbsp;is the finite element space of piecewise
constant pressures with the globally one-dimensional checker-board pattern subspace
eliminated. The proposed Stokes elements have the least number of degrees of freedom
compared to those of known stable Stokes elements. Three accuracy indications
for our elements are analyzed and numerically verified. Also, various numerous computational
results obtained by using our proposed element show excellent accuracy.</p>