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

德克萨斯大学奥斯汀分校的Ivo Babuska和捷克数学研究所的Michal Krizek之间的这个美国-捷克数学项目将研究计算数学中的可靠性问题，因为它与数学模型、模型中使用的可用信息（数据）以及所采用的数值过程有关。总的来说，这种合作应该会提高我们基于数值计算结果做出工程决策的能力。在超收敛理论的基础上，采用随机方法和最坏情况方法，通过后验估计来分析数值解的可靠性。（最坏的情况是处理一组给定的可接受输入数据，为感兴趣的信息找到边界。）具体来说，这个项目将测试：1)相对于工程决策的数学公式的可靠性；2)由数学问题的数值解导出的具有工程重要性的计算数据的可靠性。结果有望直接适用于实际工程计算，如与塑性相关的计算；弹塑性扭转;和近似摩擦的西格里尼接触问题。该应用数学项目通过使美国和中欧的顶尖专家在共同感兴趣和能力的领域结合互补的人才和集中研究资源，实现了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. ??