TITLE

SINGULARLY PERTURBED CONVECTION -- DIFFUSION PROBLEMS IN ONE DIMENSION: BOUNDS ON DERIVATIVES

AUTHOR(S)
NAUGHTON, A.; STYNES, M.
PUB. DATE
July 2009
SOURCE
Computational Methods in Applied Mathematics;2009, Vol. 9 Issue 3, p281
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A convection-dominated singularly perturbed two-point boundary problem is considered. For the numerical analysis of such problems, it is necessary to prove certain a priori bounds on the derivatives of its solution. This paper provides a survey of the ways in which such bounds can be proved, while assessing the feasibility of extending such proofs to convection-dominated partial differential equations, and also introduces a new proof based on a classical finite-difference argument of Brandt.
ACCESSION #
43536899

 

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