Cahn-Hilliard方程的拟谱逼近

该文讨论用Ｌｅｇｅｎｄｒｅ拟谱方法数值求解非线性Ｃａｈｎ Ｈｉｌｌｉａｒｄ方程的Ｄｉｒｉｃｈｌｅｔ问题．建立了其半离散和全离散逼近格式，它们保持原问题能量耗散的性质．证明了离散解的存在唯一性，并给出了最佳误差估计．数值实验也证实了我们的结果．

Legendre Collocation Approximation for Cahn-Hilliard Equation

In this paper, a Legendre collocation method for numerically solving Cahn Hilliard equations with Dirichlet boundary conditions is developed. We establish their semi discrete and fully discrete schemes that inherit the energy dissipstion property from the associated continuous problem. we prove existence and uniqueness of the numerical solution and derive the optimal error boun d s. we perform some numerical experiments which confirm our results.