Mathematical Sciences: Finite Element Method for Nonlinear Partial Differential Equations

本研究计画将研究非线性四阶 演化Cahn-Hilliard方程 一个主要的问题是， 开发一种适当的数值方法， 这两个方程的解的精确近似 和两个空间维度。 一个有效的数值方案将是 开发，以获得长时间的解决方案的二维 方程 亚稳态溶液的可能性也将是 分析了 卡恩·希利亚德方程模型，除了其他现象， 二元合金中的相分离 的结果 研究项目将在这方面和其他方面找到应用 相关的物理问题。

This research project will study the nonlinear fourth order evolutionary Cahn-Hilliard equation. A main concern will be the development of an appropriate numerical method for accurate approximation of solutions of this equation for both one and two spatial dimensions. A efficient numerical scheme will be developed to obtain long time solutions of the two dimensional equation. The possibility of metastable solutions will also be analyzed. The Cahn Hilliard equation models, among other phenomena, phase separation in binary alloys. The results of the research project will find applications in this and other related physical problems.