Singularly Perturbed Convection Diffusion Problems

University Of Maryland, College Park, College Park MD

Investigators

Abstract

Kopriva, David From: R. Bruce Kellogg [kellogg@ipst.umd.edu] Sent: Thursday, May 31, 2001 6:04 AM To: dkopriva@nsf.gov Cc: kellogg@ipst.umd.edu Subject: Proposal No: 0101563 - Abstract Proposal No: 0101563 - Abstract Some problems of mathematical and numerical analysis related to singularly perturbed boundary value problems will be studied. The mathematical problems include obtaining sharp bounds for derivatives of the solution that take into account boundary layers, interior layers, and corner singularities. The numerical problems include the development of stabilized discretizations for these singularly perturbed problems and the study of the best approximation properties of singular perturbation problems. The proposed work studies physical systems in which some quantities undergo rapid changes in certain regions. Such systems include fluid flow, where the rapid changes occur at boundary layers, shocks, and interior layers. These systems arise in the design of fluid machinery, the study of underground oil and water transport, the modeling of airflow over cars and airplanes, and other areas. The results of this research will be of use in the development of more accurate computer simulations of these systems, with consequent improvements in the design of equipment used in such real-world problems. In addition, the proposal provides for regular visits of Professor M. Stynes to the U.S.; it is planned that Prof. Stynes will interact with graduate students in mathematics who are working in related areas.