Volume 16, Issue 4
Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density

Adv. Appl. Math. Mech., 16 (2024), pp. 952-979.

Published online: 2024-05

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• Abstract

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.

65M12, 65M60

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@Article{AAMM-16-952, author = {Zhang , XinWang , DanxiaZhang , Jianwen and Jia , Hongen}, title = {Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {4}, pages = {952--979}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0121}, url = {http://global-sci.org/intro/article_detail/aamm/23118.html} }
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 -

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.

Xin Zhang, Danxia Wang, Jianwen Zhang & Hongen Jia. (2024). Error Analysis of a Pressure Penalty Scheme for the Reformulated Ericksen-Leslie System with Variable Density. Advances in Applied Mathematics and Mechanics. 16 (4). 952-979. doi:10.4208/aamm.OA-2023-0121
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