Singularly Perturbed Convection-Diffusion Problems

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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.