A parameter-uniform numerical method for a singularly perturbed convection–diffusion problem posed on an annulus. (15th November 2019)

• Record Type: Journal Article
• Authors: Hegarty, A.F.; O'Riordan, E.
• Is Part Of: Computers & mathematics with applications. Volume 78:issue 10(2019)
• Page Start: 3329
• Page End: 3344
• Publication Date: 2019-11-15
• Subjects: Singularly perturbed -- Convection–diffusion -- Shishkin mesh -- Annulus; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.05.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: A finite difference method is constructed for a singularly perturbed convection–diffusion problem posed on an annulus. The method involves combining polar coordinates, an upwind finite difference operator and a piecewise-uniform Shishkin mesh in the radial direction. Compatibility constraints are imposed on the data in the vicinity of certain characteristic points to ensure that interior layers do not form within the annulus. A theoretical parameter-uniform error bound is established and numerical results are presented to illustrate the performance of the numerical method applied to particular test problems.