| Cahn—Hilliard方程的Legendre谱逼近 |
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| 引用本文： | 叶兴德,程晓良.Cahn—Hilliard方程的Legendre谱逼近[J].计算数学,2003,25(2):157-170. |
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| 作者姓名： | 叶兴德 程晓良 |
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| 作者单位： | 浙江大学数学系,杭州,310028 |
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| 基金项目： | 国家自然科学基金(批准号:10001029)及浙江省自然科学基金资助项目. |
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| 摘 要： | 1.引 言本文我们将考虑非线性Cahn—Hilliard方程的初边值问题
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| 关 键 词： | Cahn－Hilliard方程 Legendre谱逼近 初边值问题 广义Ginzberg－Landau自由能量泛函 Neumann问题 混合形式 离散格式 Lyapunov泛函 最佳误差估计 |
| 修稿时间： | 2000年11月1日 |
LEGENDRE SPECTRAL APPROXIMATION FOR CAHN-HILLIARD EQUATION |
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| Ye Xingde Cheng Xiaoliang.LEGENDRE SPECTRAL APPROXIMATION FOR CAHN-HILLIARD EQUATION[J].Mathematica Numerica Sinica,2003,25(2):157-170. |
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| Authors: | Ye Xingde Cheng Xiaoliang |
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| Institution: | Ye Xingde Cheng Xiaoliang (Department of Mathematics, Zhejiang University at Xixi campus, Hangzhou, 310028) |
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| Abstract: | In this paper, a Legendre spectral method for numerically solving Cahn-Hilliard equations with Neumann boundary conditions is developed. We establish their semi-discrete and fully discrete schemes that inherit the energy dissipation property and mass conservation property from the associated continuous problem, we prove the existence and uniqueness of the numerical solution and derive the optimal error bounds, we perform some numerical experiments which confirm our results. |
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| Keywords: | Cahn-Hilliard Equation Legendre spectral method |
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