Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations

Authors:
T. Linß
Affiliations:
Technische Universität Dresden, Institut für Numerische Mathematik, 01062, Dresden, Germany
Venue:
Computing
Year:
2007

Citing 0
Cited 2

An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems

Numerical Analysis and Its Applications
Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems

SIAM Journal on Numerical Analysis

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Abstract

We study a system of coupled convection-diffusion equations. The equations have diffusion parameters of different magnitudes associated with them which give rise to boundary layers at either boundary. An upwind finite difference scheme on arbitrary meshes is used to solve the system numerically. A general error estimate is derived that allows to immediately conclude robust convergence – w.r.t. the perturbation parameters – for certain layer-adapted meshes, thus improving and generalising previous results [4]. We present the results of numerical experiments to illustrate our theoretical findings.