Workshop on Functional Analytic Methods in Error Prediction with Applications

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This project provides travel and subsistence support for participants in the workshop "Functional Analytic Methods in Error Prediction with Applications" held at the University of Wyoming on June 13-17, 2016. The workshop is part of an annual activity spearheaded by the Rocky Mountain Mathematics Consortium (RMMC). The workshop is aimed at exposing graduate students and junior researchers to recent progress in computational sciences, particularly in error estimation techniques utilized in a class of multi-physics and multi-scale problems inheriting various levels of uncertainty. The workshop is designed to be strongly interdisciplinary. Workshop presentations and lectures are a blend of colloquium type and more in-depth style, with the intention of allowing junior participants to gain knowledge that are potentially useful in their future endeavors, and at the same time giving more experienced participants ample opportunity to initiate research collaboration.Any numerical approximation/simulation for solving mathematical problems contains some errors. These errors are often functionally dependent on some parameters associated with the method. Formally, a robust numerical method should exhibit a behavior in which the errors vanish in the limiting process associated with the parameters. A standard practice is to estimate the errors in terms of the parameters and some regularity assumptions of the original problems. Unfortunately, many applications prevent imposing those theoretical assumptions, thereby creating a need to monitor the errors in real time simulation. Having this availability will enhance the robustness of the approximation in the predictive simulation. Furthermore, a closely related aspect to error estimation is quantifying the uncertainty that can be present both in the original problem and in the techniques employed to approximate it. The appropriate strategy to tackle this is multifaceted, involving reliance on sophisticated mathematical and statistical tools. This workshop provides a forum for researchers to address all these issues. More information can be found at the workshop website: www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/