TY - JOUR
T1 - Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density
AU - Zhang , Xin
AU - Wang , Danxia
AU - Zhang , Jianwen
AU - Jia , Hongen
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 952
EP - 979
PY - 2024
DA - 2024/05
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2023-0121
UR - https://global-sci.org/intro/article_detail/aamm/23118.html
KW - Variable density, constraint-preserving, Ericksen-Leslie, error analysis.
AB - <p style="text-align: justify;">Numerical approximation of the Ericksen-Leslie system with variable density is considered in this paper. The spherical constraint condition of the orientation
field is preserved by using polar coordinates to reformulate the system. The equivalent new system is computationally cheaper because the vector function of the orientation field is replaced by a scalar function. An iteration penalty method is applied
to construct a numerical scheme so that stability is improved. We first prove that the
scheme is uniquely solvable and unconditionally stable in energy. Then we show that
this scheme is of first-order convergence rate by rigorous error estimation. Finally,
some numerical simulations are performed to illustrate the accuracy and effectiveness
of the scheme.</p>