The Effective Numerical Solution of Elliptic Equations

椭圆方程的有效数值解

• 批准号: 9501256
• 负责人: Seymour Parter
• 金额: $ 6.1万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501256&HistoricalAwards=false
• 关键词: Effective; Numerical; Solution; Elliptic; Equations

9501256 Parter The major efforts of this research project are twofold: (1) The study of preconditioning strategies for the Chebyshev spectral collocation method for elliptic boundary-value problems, and (2) the study of first order least squares methods for equations of practical import. The equations of linear elasticity are of special importance and interest. The significance of a- posteriori error estimates for these problems is balanced by the need for deeper a-priori error estimates. The difficulty in obtaining a-priori error estimates stems from the explicit appearance of the divergence operator in these problems. Similar difficulties appear in the study of numerical methods for the Stokes equations. There are many important practical problems which arise in fluid flow and elasticity which lead to problems which must be solved on the computer. The solutions of these problems are then approximations to solutions of elliptic boundary value problems. Most of the research in this area has emphasized finding a computer problem whose solution is indeed a very good approximation to the solution of the elliptic problem. Having done that, one must still find efficient and relatively cheap methods to solve the computer problem. This last, very practical problem, is the focus of the research in this project.

小行星9501256 本课题的主要工作有两个方面：（1）研究了 Chebyshev谱配置法的预处理策略 （2）一阶最小问题的研究 平方法方程的实际进口。 线性方程组 弹性具有特殊的重要性和意义。 这些问题的后验误差估计的重要性是平衡的需要， 更深的先验误差估计。 获得先验误差的困难 估计源于显式外观的发散运算符， 这些问题 类似的困难也出现在数字化的研究中。 Stokes方程的方法。 在流体流动中出现了许多重要的实际问题， 弹性导致必须在计算机上解决的问题。 这些问题的解近似于 椭圆边值问题 这一领域的大部分研究都是 我强调找到一个计算机问题，它的解决方案确实是一个非常 椭圆问题的解的一个很好的近似。 做了 因此，人们仍然必须找到有效和相对便宜的方法来解决这个问题。 电脑问题。 这最后一个非常实际的问题，是本书的重点。 在这个项目中的研究。