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

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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. ??