Singularly Perturbed Convection Diffusion Problems

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Kopriva, DavidFrom: R. Bruce Kellogg [kellogg@ipst.umd.edu]Sent: Thursday, May 31, 2001 6:04 AMTo: dkopriva@nsf.govCc: kellogg@ipst.umd.eduSubject: Proposal No: 0101563 - AbstractProposal No: 0101563 - AbstractSome problems of mathematical and numerical analysis related tosingularly perturbed boundary value problems will be studied. Themathematical problems include obtaining sharp bounds for derivatives ofthe solution that take into account boundary layers, interior layers, andcorner singularities. The numerical problems include the development ofstabilized discretizations for these singularly perturbed problems andthe study of the best approximation properties of singular perturbationproblems.The proposed work studies physical systems in which some quantitiesundergo rapid changes in certain regions. Such systems include fluid flow,where the rapid changes occur at boundary layers, shocks, and interiorlayers. These systems arise in the design of fluid machinery, the studyof underground oil and water transport, the modeling of airflow overcars and airplanes, and other areas. The results of this research willbe of use in the development of more accurate computer simulations ofthese systems, with consequent improvements in the design of equipmentused in such real-world problems. In addition, the proposal providesfor regular visits of Professor M. Stynes to the U.S.; it is plannedthat Prof. Stynes will interact with graduate students in mathematics whoare working in related areas.