A Scalar Auxiliary Variable Unfitted FEM for the Surface Cahn–Hilliard Equation

被引：0
作者：
Olshanskii M. [1 ]
Palzhanov Y. [1 ]
Quaini A. [1 ]
机构：
[1] Department of Mathematics, University of Houston, 3551 Cullen Blvd, Houston, 77204, TX
来源：
Journal of Scientific Computing | 2023年 / 97卷 / 03期
基金：
美国国家科学基金会;
关键词：
Adaptive time-stepping; Membrane phase separation; SAV approach; Surface Cahn–Hilliard equation; TraceFEM;
D O I：
10.1007/s10915-023-02370-8
中图分类号：
学科分类号：
摘要：
The paper studies a scalar auxiliary variable (SAV) method to solve the Cahn–Hilliard equation with degenerate mobility posed on a smooth closed surface Γ . The SAV formulation is combined with adaptive time stepping and a geometrically unfitted trace finite element method (TraceFEM), which embeds Γ in R3 . The stability is proven to hold in an appropriate sense for both first- and second-order in time variants of the method. The performance of our SAV method is illustrated through a series of numerical experiments, which include systematic comparison with a stabilized semi-explicit method. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
相关论文
共 46 条
[1]  
Akrivis G., Li B., Li D., Energy-decaying extrapolated RK-SAV methods for the Allen–Cahn and Cahn–Hilliard equations, SIAM J. Sci. Comput., 41, 6, pp. A3703-A3727, (2019)
[2]  
Bandekar A., Zhu C., Gomez A., Menzenski M.Z., Sempkowski M., Sofou S., Masking and triggered unmasking of targeting ligands on liposomal chemotherapy selectively suppress tumor growth in vivo, Mol. Pharm., 10, 1, pp. 152-160, (2013)
[3]  
Burman E., Hansbo P., Larson M.G., A stabilized cut finite element method for partial differential equations on surfaces: the Laplace–Beltrami operator, Comput. Methods Appl. Mech. Eng., 285, pp. 188-207, (2015)
[4]  
Cahn J.W., On spinodal decomposition, Acta Metall., 9, 9, pp. 795-801, (1961)
[5]  
Cahn J.W., Hilliard J.E., Free energy of a nonuniform system. I. interfacial free energy, J. Chem. Phys., 28, 2, pp. 258-267, (1958)
[6]  
Chen C., Yang X., Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn–Hilliard model, Comput. Methods Appl. Mech. Eng., 351, pp. 35-59, (2019)
[7]  
Chen H., Mao J., Shen J., Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows, Numer. Math., 145, 1, pp. 167-196, (2020)
[8]  
Cheng Q., Shen J., Yang X., Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach, J. Sci. Comput., 78, pp. 1467-1487, (2019)
[9]  
DROPS Package
[10]  
Dziuk G., Elliott C.M., Finite element methods for surface PDEs, Acta Numer., 22, pp. 289-396, (2013)
12345