Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters

This paper discusses the numerical solution of linear 1-D singularly perturbed parabolic convection-diffusion-reaction problems with two small parameters using a moving mesh-adaptive algorithm which adapts meshes to boundary layers. The meshes are generated by the equidistribution of a special posit...

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Bibliographic Details
Published inBIT Numerical Mathematics Vol. 56; no. 1; pp. 51 - 76
Main Authors Das, Pratibhamoy, Mehrmann, Volker
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2016
Subjects
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Parabolic partial differential equation
Singularly perturbed problem
Uniform convergence
65N12
Convection-diffusion-reaction problem
65M06
65N50
Adaptive mesh
Moving mesh method
Mesh equidistribution
65M50
Upwind scheme
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Summary:This paper discusses the numerical solution of linear 1-D singularly perturbed parabolic convection-diffusion-reaction problems with two small parameters using a moving mesh-adaptive algorithm which adapts meshes to boundary layers. The meshes are generated by the equidistribution of a special positive monitor function. Parameter independent uniform convergence is shown for a class of model problems and the obtained result hold even for the limiting case where the perturbation parameters are zero. Numerical experiments are presented that illustrate the first-order parameter uniform convergence, and also show that the new approach has better accuracy compared with current methods.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-015-0559-8