Mathematical Sciences: Reliability of Computational Analysis

数学科学：计算分析的可靠性

• 批准号: 9501841
• 负责人: Ivo Babuska
• 金额: --
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501841&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Reliability; Computational; Analysis

9501841 Babuska The project concentrates on basic problems of computational mathematics and its applications in mechanics. The following major directions will be addressed: 1) The problem of a-posteriori error estimation and adaptive procedures; 2) Various types of recovery of data of interest from the finite element solution; 3) The problem of analysis of the uncertainties in the input data on the solution, of stochastic or maximal character; and 4) Computational aspects of the h-p version of the finite element method. Theoretical, computational, and implementational aspects mentioned above will be addressed. Computational analysis has become the major tool in science and engineering, because of the availability of powerful computers. The major problems are the assessment of the reliability of the computed data and the design of adaptive approaches when the computer selects by itself the most effective way to compute reliability data of interest. This project concentrates on these essential problems. It will address the reliability of the numerical solution of partial differential equations and of the models described by the equations, as well as adaptive approaches leading to the best results.

9501841巴布斯卡该项目专注于计算数学的基本问题及其在力学中的应用。将讨论以下主要方向：1)后验误差估计和自适应程序的问题；2)从有限元解中恢复感兴趣的各种类型的数据；3)分析输入数据中关于解的不确定性的问题，具有随机性或极大性；以及4)h-p形式的有限元方法的计算方面。上面提到的理论、计算和实现方面将被讨论。由于功能强大的计算机的出现，计算分析已经成为科学和工程中的主要工具。主要问题是评估计算数据的可靠性，以及当计算机自己选择最有效的方法来计算感兴趣的可靠性数据时，自适应方法的设计。这个项目集中在这些基本问题上。它将讨论偏微分方程数值解的可靠性和方程所描述的模型的可靠性，以及导致最佳结果的自适应方法。