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

该奖项是根据国际博士后研究员计划颁发的，该计划使美国科学家和工程师能够在外国公认的卓越中心进行为期3至12个月的研究。该项目的奖项提供了联合研究的机会，并提供了使用国外独特或互补的设施、专业知识和实验条件的机会。该奖项将支持佐治亚理工学院的Donald EStep博士与瑞典哥德堡查尔默斯理工大学的Claes Johnson教授合作进行为期12个月的博士后研究访问。该项目涉及发展奇摄动反应扩散方程组的自适应有限元方法的数学理论。这些方程给数学家带来了许多技术挑战，同时也代表了应用科学中的许多重要模型。由于此类问题的解决方案通常具有多尺度行为，并且需要一系列参数值的准确结果，因此标准的数值技术和分析是不够的。EStep博士和Johnson教授希望通过开发一种基于后验和先验误差界的错误控制来克服这些困难，该错误控制将指示如何控制错误并给出了计算的稳健性度量。最终目标是公开发布一个代码，该代码可以用最少的用户界面解决一般问题。该奖项建议为佐治亚理工学院提供国际旅行、为期12个月的津贴和行政费用。

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.