Singularly Perturbed Convection-Diffusion Problems

数学科学：奇摄动对流扩散问题本项目将在多边形域上建立奇摄动对流扩散问题解的导数的尖锐点界，重点研究边界层与角点奇点之间的相互作用，并假设数据的任意光滑性。这项工作还将发展这些界限在数值算法中的应用。本项目研究了一些用于模拟流体流动和输运的微分方程。重点讨论由边界层和拐角奇点引起的快速过渡解的性质。这些性质与潜在的解结构、扩散、对流和边界不规则（角）的竞争效应有关，有助于这种结构，以及由此产生的解的数值近似性。该奖项支持爱尔兰科克大学学院的马丁·斯泰恩斯和南卡罗莱纳大学的布鲁斯·凯洛格之间的合作研究旅行。

NSF Award Abstract - DMS-0303684Mathematical Sciences: Singularly Perturbed Convection-diffusion ProblemsAbstract0303684 Kellogg This project will establish establish sharp pointwise bounds on the derivatives of the solution of a singularly perturbed convection-diffusion problem in a polygonal domain, with an emphasis on the interaction between boundary layers and corner singularities and under the assumption of arbitrary smoothness of the data. The work will also develop applications of these bounds in numerical algorithms.This project investigates some differential equations of the type used in modeling fluid flow and transport. Emphasis is placed on properties of solutions with rapid transitions arising from boundary layers and corner singularities. These properties relate to the underlying solution structure, the competing effects of diffusion, convection and boundary irregularities (corners) contributing to this structure, and the resulting numerical approximability of the solutions. The award supports travel for collaborative research between Martin Stynes, University College, Cork, Ireland, and Bruce Kellogg, University of South Carolina.