Mathematical Sciences: Reliability of Computational Analysis

9501841 Babuska该项目集中研究计算数学的基本问题及其在力学中的应用。主要研究方向如下：1)后验误差估计和自适应过程问题；2)从有限元解中恢复各种类型的感兴趣数据；3)输入数据中的不确定性对解的分析问题，是随机的还是极大的；4) hp版有限元法的计算方面。上面提到的理论、计算和实现方面将被解决。由于强大的计算机的可用性，计算分析已成为科学和工程中的主要工具。当计算机自行选择最有效的方法来计算感兴趣的可靠性数据时，主要的问题是计算数据的可靠性评估和自适应方法的设计。这个项目集中在这些基本问题上。它将讨论偏微分方程的数值解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。

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.