Mathematical Sciences: Reliability of Computational Analysis

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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.