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Uniformly Convergent Difference Scheme for a Singularly Perturbed Problem of Mixed Parabolic-Elliptic Type

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Numerical Analysis and Its Applications (NAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3401))

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Abstract

One dimensional singularly perturbed problem with discontinuous coefficients is considered. The domain is partitioned into two subdomains and in one of them the we have parabolic reaction-diffusion problem and in the other one elliptic convection-diffusion-reaction equation.The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We established almost second-order in space variable global pointwise convergence that is uniform with respect to the perturbation parameter. Numerical experiments support the theoretical results.

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References

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Informatics, University of Rousse, Studentska str.8, 7017, Rousse, Bulgaria

    Iliya A. Brayanov

Authors
  1. Iliya A. Brayanov
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Editor information

Editors and Affiliations

  1. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, P.O. Box, Hong Kong

    Zhilin Li

  2. Department of Mathematics, University of Rousse, 7017, Rousse, Bulgaria

    Lubin Vulkov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2005 Springer-Verlag Berlin Heidelberg

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Brayanov, I.A. (2005). Uniformly Convergent Difference Scheme for a Singularly Perturbed Problem of Mixed Parabolic-Elliptic Type. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_24

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  • DOI: https://doi.org/10.1007/978-3-540-31852-1_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24937-5

  • Online ISBN: 978-3-540-31852-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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