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

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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.

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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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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Federal Republic of Germany

    Pratibhamoy Das & Volker Mehrmann

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  1. Pratibhamoy Das
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  2. Volker Mehrmann
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Corresponding author

Correspondence to Volker Mehrmann.

Additional information

Communicated by Mechthild Thalhammer.

This research was supported by the Einstein Foundation and International Mathematical Union program.

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Das, P., Mehrmann, V. Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters. Bit Numer Math 56, 51–76 (2016). https://doi.org/10.1007/s10543-015-0559-8

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  • DOI: https://doi.org/10.1007/s10543-015-0559-8

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