U.S.-Czech Mathematics Research on Reliability Problems in Computational Mechanics

INT 9724783 Babuska 这个美国-捷克数学项目之间的伊沃Babuska的得克萨斯大学，奥斯汀，和Michal Krizek的捷克数学研究所，布拉格，将审查问题的可靠性计算数学，因为它涉及到数学模型，可用的信息，在这种模型（数据），和数值程序。 总的来说，这种合作应该产生的工作，将提高我们的能力，使工程决策的基础上的数值计算的结果。 利用随机方法和最坏情况下的方法，研究人员打算分析的可靠性的数值解（S）的后验估计的超收敛理论的基础上。 (The最坏情况方法涉及使用给定的一组可接受的输入数据来找到感兴趣的信息的界限。 具体而言，该项目将测试：1）数学公式在工程决策方面的可靠性; 2）通过数学问题的数值解得出的具有工程重要性的计算数据的可靠性。 结果预计将直接适用于实际的工程计算，如与塑性，弹塑性扭转和Signorini接触问题与近似摩擦。 这个应用数学项目实现了通过使美国和中欧的领先专家能够联合收割机互补人才和在共同感兴趣和能力的领域汇集研究资源来推进基础科学知识的计划目标。 ??

INT 9724783 Babuska This U.S.-Czech mathematics project between Ivo Babuska of the University of Texas, Austin, and Michal Krizek of the Czech Mathematics Institute, Prague, will examine the problem of reliability in computational mathematics as it relates to mathematical models, available information used in such models (data), and the numerical procedures employed. Overall, this collaboration should yield work that will improve our ability to make engineering decisions based on the outcome of numerical computations. Using a stochastic approach and a worst case approach, the researchers intend to analyze the reliability of the numerical solution(s) by an a-posteriori estimation on the basis of the superconvergence theory. (The worst case approach involves working with a given set of admissible input data to find bounds for the information of interest.) Specifically, this project will test: 1) reliability of mathematical formulations with respect to engineering decisions; and 2) reliability of computed data of engineering importance that is derived by a numerical solution of the mathematical problem. Results are expected to be directly applicable to practical engineering calculations such as those associated with plasticity; elastoplastic torsion; and the Signorini contact problem with approximate friction. This applied mathematics project fulfills the program objective of advancing basic scientific knowledge by enabling leading experts in the United States and Central Europe to combine complementary talents and pool research resources in areas of mutual interest and competence. ??