International Postdoctoral Fellows Program: Numerical Analysis of Reaction-Diffusion Equations

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This award is under the International Postdoctoral Fellows Program, which enables U.S. scientists and engineers to conduct three to twelve months of research at foreign centers of proven excellence. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twelve-month postdoctoral research visit by Dr. Donald Estep of the Georgia Institute of Technology to work with Professor Claes Johnson at Chalmers University of Technology in Gothenburg, Sweden. This project involves the development of a mathematical theory for adaptive finite element methods for systems of singularly-perturbed reaction-diffusion equations. These equations offer many technical challenges to mathematicians while representing many important models in applied science. Because solutions of such problems typically have multiply-scaled behavior and because accurate results are needed for a range of parameter values, standard numeric techniques and analysis are inadequate. Dr. Estep and Professor Johnson hope to overcome these difficulties by developing an error control based on a posteriori and a priori error bounds that will indicate how to control the error as well as give a measure of robustness to the computations. The ultimate goal is the public release of a code that can solve general problems with minimum user interface. The award recommendation provides funds to cover international travel, a stipend for twelve months and administrative costs for Georgia Tech.