TY - JOUR
T1 - Semi-Discrete Predictor-Multicorrector FEM Algorithms for the 2D/3D Unsteady Incompressible Micropolar Fluid Equations
AU - Bi , Xiaowei
AU - Liu , Demin
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1519
EP - 1548
PY - 2024
DA - 2024/10
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0256
UR - https://global-sci.org/intro/article_detail/aamm/23477.html
KW - Micropolar fluid equations, predictor-multicorrector algorithm, finite element method, error estimates.
AB - <p style="text-align: justify;">In this paper, the first-order and second-order semi-discrete predictor-multicorrector (PMC) algorithms to solve the 2D/3D unsteady incompressible micropolar fluid equations (IMNSE) are proposed. In the algorithms, the first-order and
second-order BDF formulas are adopted to approximate the time derivative terms. At
each time step, two elliptical sub-problems with Dirichlet conditions are solved at the
prediction step, the strategy of projection about linear momentum equation with additional viscosity term and the elliptical sub-problems about angular momentum are
solved at the multicorrection step. Furthermore, the unconditional stability and error
estimates of the first-order scheme are proved theoretically. Numerical experiments
are carried out to show the effectiveness of the algorithms.</p>