Mathematical Sciences: Finite Element Method for Nonlinear Partial Differential Equations

数学科学：非线性偏微分方程的有限元法

• 批准号: 8802828
• 负责人: Donald French
• 金额: $ 0.92万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802828&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Finite; Element; Method

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.

本研究项目将研究非线性四阶发展Cahn-Hilliard方程。主要关注的将是发展一种适当的数值方法来精确逼近该方程的一维和二维的解。将开发一种有效的数值格式来获得二维方程的长时间解。还将分析亚稳态解决方案的可能性。除其他现象外，Cahn Hilliard方程模型还包括二元合金中的相分离。该研究项目的结果将在这一问题和其他相关物理问题上得到应用。