A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation

2003 ◽  
Vol 20 (1) ◽  
pp. 65-85 ◽  
Author(s):  
Daisuke Furihata ◽  
Takayasu Matsuo
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals The Cahn–Hilliard Equation with Generalized Mobilities in Complex Geometries

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jaemin Shin ◽  
Yongho Choi ◽  
Junseok Kim
Keyword(s):  
Growth Rate ◽  
Finite Difference ◽  
Difference Scheme ◽  
Pore Size ◽  
Finite Difference Scheme ◽  
Numerical Experiments ◽  
Complex Geometries ◽  
Hilliard Equation ◽  
Controlled Porosity ◽  
Cahn Hilliard Equation

In this study, we apply a finite difference scheme to solve the Cahn–Hilliard equation with generalized mobilities in complex geometries. This method is conservative and unconditionally gradient stable for all positive variable mobility functions and complex geometries. Herein, we present some numerical experiments to demonstrate the performance of this method. In particular, using the fact that variable mobility changes the growth rate of the phases, we employ space-dependent mobility to design a cylindrical biomedical scaffold with controlled porosity and pore size.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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