Paper Info
Title
Uniform Second Order Convergence of a Complete Flux Scheme on Unstructured 1D Grids for a Singularly Perturbed Advection-Diffusion Equation and Some Multidimensional Extensions.
Abstract
The accurate and efficient discretization of singularly perturbed advection---diffusion equations on arbitrary 2D and 3D domains remains an open problem. An interesting approach to tackle this problem is the complete flux scheme (CFS) proposed by G. D. Thiart and further investigated by J. ten Thije Boonkkamp. For the CFS, uniform second order convergence has been proven on structured grids. We extend a version of the CFS to unstructured grids for a steady singularly perturbed advection---diffusion equation. By construction, the novel finite volume scheme is nodally exact in 1D for piecewise constant source terms. This property allows to use elegant continuous arguments in order to prove uniform second order convergence on unstructured one-dimensional grids. Numerical results verify the predicted bounds and suggest that by aligning the finite volume grid along the velocity field uniform second order convergence can be obtained in higher space dimensions as well.
Year
DOI
Venue
2017
10.1007/s10915-017-0361-7
J. Sci. Comput.
Keywords
Field
DocType
Singularly perturbed advection–diffusion equation, Uniform second-order convergence, Finite-volume method, Complete flux scheme, 65L11, 65L20, 65N08, 65N12
Convergence (routing),Convection–diffusion equation,Discretization,Mathematical optimization,Open problem,Mathematical analysis,Vector field,Finite volume method,Mathematics,Piecewise,Grid
Journal
Volume
Issue
ISSN
72
1
1573-7691
Citations 
PageRank 
References 
0
0.34
4
Authors
2
Name
Order
Citations
PageRank
Patricio Farrell110.70
Alexander Linke29212.29