Mathematical Sciences: Numerical Approximation of Strongly Nonlinear and Constrained Problems

数学科学：强非线性和约束问题的数值逼近

• 批准号: 8805218
• 负责人: Ricardo Nochetto
• 金额: $ 2.81万
• 依托单位: University of Maryland, College Park
• 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: 1988-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805218&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Numerical; Approximation; Strongly

This research will consider the numerical analysis of strongly nonlinear problems including free boundary problems, constrained problems such as Stokes flow, and the Hamilton-Jacobi equations. Linearization techniques based on nonlinear Chernoff formulae will be investigated, and nonlinear algorithms for both parabolic and eliptic problems will be analyzed with particular emphasis on accuracy in nonenergy spaces and splitting algorithms. The impact of local mesh refinements in reducing computational labor for a given accuracy will be considered. Work analyzing the pointwise accuracy of mixed finite element methods will be continued. This work will combine and interrelate theory and numerical methods. It should increase understanding of both the numerical techniques and the motivating physical situations.

本研究将考虑的数值分析， 强非线性问题包括自由边界问题， 斯托克斯流和汉密尔顿-雅可比等约束问题 方程 基于非线性滤波器的线性化技术 公式将被调查，和非线性算法， 抛物和椭圆问题将进行分析， 强调非能量空间和分裂的准确性 算法 局部网格细化对减少 将考虑给定精度的计算工作量。 混合有限元逐点精度分析 方法将继续。 这项工作将联合收割机和相互关联的理论和数值 方法. 它应该增加对数字和 技术和激励身体的情况。