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Numerical Approximation of the Space Fractional Cahn-Hilliard Equation
- Source :
- Mathematical Problems in Engineering, Vol 2019 (2019)
- Publication Year :
- 2019
- Publisher :
- Hindawi Limited, 2019.
-
Abstract
- In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case.
- Subjects :
- Backward differentiation formula
Article Subject
Discretization
lcsh:Mathematics
General Mathematics
General Engineering
010103 numerical & computational mathematics
lcsh:QA1-939
01 natural sciences
010101 applied mathematics
symbols.namesake
Fourier transform
Numerical approximation
lcsh:TA1-2040
Regularization (physics)
symbols
Applied mathematics
0101 mathematics
lcsh:Engineering (General). Civil engineering (General)
Cahn–Hilliard equation
Mathematics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2019
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....7ac3215855e3e941df13ef0a56ef1d0e