Professor Martin Stynes   School of Mathematical Sciences   University College Cork

Abstract: In convection-diffusion problems, transport processes dominate while diffusion effects are confined to a relatively small part of the domain. This state of affairs means that one cannot rely on the formal ellipticity of the differential operator to ensure the convergence of standard numerical algorithms. Thus new ideas and approaches are required.

The survey begins by examining the asymptotic nature of solutions to stationary convection-diffusion problems. This provides a suitable framework for the understanding of these solutions and the difficulties that numerical techniques will face. A priori bounds on derivatives and decompositions of solutions are examined. This investigation of the nature of the solutions to convection-diffusion problems motivates various numerical methods that are expressly designed for convection-diffusion problems; these are presented and extensively discussed. They include finite difference methods, finite element methods and the use of special meshes.

About the Speaker: Professor Martin Stynes is interested in the design and analysis of numerical methods for singularly perturbed differential equations. This includes convection-diffusion problems, linearized Navier-Stokes equations and the like. He is a member of the editorial boards of the journals Advances in Computational Mathematics,  Advances in Numerical Analysis, Computational Methods in Applied Mathematics, International Journal of Computing Science and Mathematics, and theMathematical Proceedings of the Royal Irish Academy.

Date&Time: October 8 - October 11, 2012 (from Monday to Thursday) 9:00-11:30a.m.
Location: 606 Conference Room, No.3 Heqing Road, Haidian District