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BIT Numerical Mathematics

, Volume 56, Issue 1, pp 51–76 | Cite as

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

  • Pratibhamoy Das
  • Volker MehrmannEmail author
Article

Abstract

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.

Keywords

Parabolic partial differential equation Convection-diffusion-reaction problem Adaptive mesh Moving mesh method Mesh equidistribution Singularly perturbed problem Upwind scheme Uniform convergence 

Mathematics Subject Classification

65M06 65N12 65N50 65M50 

Notes

Acknowledgments

The first author expresses his thank to the Einstein Foundation and International Mathematical Union fellowship program for supporting his research visit at TU Berlin.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinFederal Republic of Germany

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