Stability and convergence of the spectral Galerkin method for the Cahn-Hilliard equation

2008 ◽  
Vol 24 (6) ◽  
pp. 1485-1500 ◽  
Author(s):  
Yinnian He ◽  
Yunxian Liu
Keyword(s):  
Galerkin Method ◽  
Stability And Convergence ◽  
Hilliard Equation ◽  
Spectral Galerkin Method ◽  
Cahn Hilliard Equation

A discontinuous Galerkin method for the Cahn–Hilliard equation

2006 ◽  
Vol 218 (2) ◽  
pp. 860-877 ◽  
Author(s):  
Garth N. Wells ◽  
Ellen Kuhl ◽  
Krishna Garikipati
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

A discontinuous Galerkin method for the Cahn-Hilliard equation

2005 ◽  
Vol 18 (1-2) ◽  
pp. 113-126 ◽  
Author(s):  
S. M. Choo ◽  
Y. J. Lee
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation

2013 ◽  
Vol 3 (4) ◽  
pp. 333-351 ◽  
Author(s):  
Lizhen Chen ◽  
Chuanju Xu
Keyword(s):  
Lower Order ◽  
Neumann Boundary ◽  
Mass Conservation ◽  
Spectral Element ◽  
Stability And Convergence ◽  
Time Step ◽  
Fully Discrete ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation ◽  
The Stability

AbstractWe propose and analyse a class of fully discrete schemes for the Cahn-Hilliard equation with Neumann boundary conditions. The schemes combine large-time step splitting methods in time and spectral element methods in space. We are particularly interested in analysing a class of methods that split the original Cahn-Hilliard equation into lower order equations. These lower order equations are simpler and less computationally expensive to treat. For the first-order splitting scheme, the stability and convergence properties are investigated based on an energy method. It is proven that both semi-discrete and fully discrete solutions satisfy the energy dissipation and mass conservation properties hidden in the associated continuous problem. A rigorous error estimate, together with numerical confirmation, is provided. Although not yet rigorously proven, higher-order schemes are also constructed and tested by a series of numerical examples. Finally, the proposed schemes are applied to the phase field simulation in a complex domain, and some interesting simulation results are obtained.

A stabilized hybrid discontinuous Galerkin method for the Cahn-Hilliard equation

2021 ◽  
pp. 114025
Author(s):  
Emmanuel Y. Medina ◽  
Elson M. Toledo ◽  
Iury Igreja ◽  
Bernardo M. Rocha
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation
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