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，使 美国科学家和工程师将进行三次 在国外中心进行为期12个月的研究 证明卓越。 该计划的奖项 提供联合研究的机会， 使用独特或互补的设施， 国外的实验条件和经验。 该奖项将支持为期12个月的 Donald Estep博士的博士后研究访问 格鲁吉亚理工学院的校长 和查尔默斯的克莱斯约翰逊教授 瑞典哥德堡的科技大学。 该项目涉及开发一个 自适应有限元数学理论 奇异摄动系统方法 反应扩散方程 这些方程 提出了许多技术挑战， 数学家虽然代表了许多 应用科学中的重要模型。 因为 这些问题的解决方案通常具有 多尺度行为，因为准确 需要一系列参数的结果 值、标准数值技术和 分析不够。 Estep博士和 约翰逊教授希望克服这些困难 开发错误控制的困难 基于后验和先验误差界 这将表明如何控制错误， 同时也给了一个衡量 计算。 最终目的是公众 发布一个代码，可以解决一般 最小用户界面的问题。 授标建议提供资金， 包括国际旅行， 12个月和行政费用 格鲁吉亚理工大学

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.