Abstract
Linear singularly perturbed ordinary differential equations of convection diffusion type are considered. The convective coefficient varies in scale across the domain which results in interior layers appearing in areas where the convective coefficient decreases from a scale of order one to the scale of the diffusion coefficient. Appropriate parameter-uniform numerical methods are constructed. Numerical results are given to illustrate the theoretical error bounds established.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
de Falco, C., O’ Riordan, E.: A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations. Numerical Algorithms 5(1), 107–127 (2011)
Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Robust computational techniques for boundary layers. Chapman and Hall/CRC Press, Boca Raton, U.S.A (2000)
Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’ Riordan, E., Shishkin, G.I.: Singularly perturbed convection diffusion problems with boundary and weak interior layers. Journal Computational and Applied Mathematics 166(1), 133–151 (2004)
O’ Riordan, E., Quinn, J.: Parameter-uniform numerical methods for some Linear and Nonlinear Singularly Perturbed Convection Diffusion Boundary Turning Point Problems. BIT Numerical Mathematics 51, 317–337 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
O’Riordan, E., Quinn, J. (2013). Multiscale Convection in One Dimensional Singularly Perturbed Convection–Diffusion Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-41515-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41514-2
Online ISBN: 978-3-642-41515-9
eBook Packages: Computer ScienceComputer Science (R0)