Fourier spectral approximation for the convective Cahn-Hilliard equation in 2D cas
Xiaopeng Zhao, Fengnan Liu
TL;DR
This paper develops Fourier spectral methods for numerically solving the 2D convective Cahn-Hilliard equation, establishing schemes with proven existence, uniqueness, and optimal error bounds.
Contribution
It introduces semi-discrete and fully discrete Fourier spectral schemes specifically for the 2D convective Cahn-Hilliard equation, with rigorous analysis.
Findings
Established existence and uniqueness of solutions.
Proved optimal error bounds for the schemes.
Validated the effectiveness of the spectral methods.
Abstract
In this paper, we consider the Fourier spectral method for numerically solving the 2D convective Cahn-Hilliard equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error bound are also considered.
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Taxonomy
TopicsSolidification and crystal growth phenomena · Advanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods