Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation

2022 ◽  
Vol 419 ◽  
pp. 126880
Author(s):  
Yaxiang Li ◽  
Jiangxing Wang
Keyword(s):  
Convergence Analysis ◽  
Unconditional Convergence ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

A Uniquely Solvable, Energy Stable Numerical Scheme for the Functionalized Cahn–Hilliard Equation and Its Convergence Analysis

2018 ◽  
Vol 76 (3) ◽  
pp. 1938-1967 ◽  
Author(s):  
Wenqiang Feng ◽  
Zhen Guan ◽  
John Lowengrub ◽  
Cheng Wang ◽  
Steven M. Wise ◽  
...  
Keyword(s):  
Convergence Analysis ◽  
Numerical Scheme ◽  
Hilliard Equation ◽  
Energy Stable ◽  
Cahn Hilliard Equation

scholarly journals The Spectral Method for the Cahn-Hilliard Equation with Concentration-Dependent Mobility

2012 ◽  
Vol 2012 ◽  
pp. 1-35 ◽  
Author(s):  
Shimin Chai ◽  
Yongkui Zou
Keyword(s):  
Theoretical Analysis ◽  
Convergence Analysis ◽  
Spectral Method ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Type Equation ◽  
Euler Method ◽  
Implicit Euler Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

This paper is concerned with the numerical approximations of the Cahn-Hilliard-type equation with concentration-dependent mobility. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method for the space and the implicit Euler method for the time. Numerical experiments are carried out to illustrate the theoretical analysis.

scholarly journals On the sharp interface limit of a model for phase separation on biological membranes

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Abels ◽  
Johannes Kampmann
Keyword(s):  
Lipid Raft ◽  
Cell Membranes ◽  
System Modeling ◽  
Bulk Diffusion ◽  
Type Equation ◽  
Sharp Interface ◽  
Interface Problem ◽  
Hilliard Equation ◽  
System A ◽  
Cahn Hilliard Equation

AbstractWe rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed in [H. Garcke, J. Kampmann, A. Rätz and M. Röger, A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes, Math. Models Methods Appl. Sci. 26 2016, 6, 1149–1189] to weak (varifold) solutions of the corresponding sharp-interface problem for a suitable subsequence. In the system a Cahn–Hilliard type equation on the boundary of a domain is coupled to a diffusion equation inside the domain. The proof builds on techniques developed in [X. Chen, Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom. 44 1996, 2, 262–311] for the corresponding result for the Cahn–Hilliard equation.

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