Skip to main content
SpringerLink
Log in
Book cover

International Conference on Large-Scale Scientific Computing

LSSC 2003: Large-Scale Scientific Computing pp 429–437Cite as

Finite Volume Difference Methods for Convection-Dominated Problems with Interface

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2907))

Abstract

In this paper we develop monotone finite volume difference schemes for a two dimensional singularly perturbedconvection-diffusion elliptic problem with interface. Theoretical results and numerical experiments for fitted mesh (Shishkin’s mesh) approximations are presented.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andreev, V.B.: Anisotropic estimates for the discrete Green’s function of a monotone difference operator in the singularly perturbed case and its application. Preprint TU Dresden, Math-NM-06-2000 (2000)

    Google Scholar 

  2. Braianov, I.A.: Finite volume difference scheme for a stiff elliptic reaction-diffusion problem with line interface. In: Vulkov, L.G., Waśniewski, J., Yalamov, P. (eds.) NAA 2000. LNCS, vol. 1988, pp. 117–124. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Braianov, I.A., Vulkov, L.G.: Uniform in a small parameter convergence of Samarskii’s monotone scheme and its modification for the convection-diffusion equation with a concentrated source. Comput. Math. Math. Phys. 40(4), 534–550 (2000)

    MATH  MathSciNet  Google Scholar 

  4. Ewing, R.E., Lazarov, R.D., Vassilevski, P.S.: Local refinement techniques for elliptic problems on cell centered grids. I. Error estimates. Math. Comp. 56(194), 437–461 (1991)

    MATH  MathSciNet  Google Scholar 

  5. Farrel, P.A., Hegarty, A.F., Miller, J.J., O’Riordan, E., Shishkin, G.I.: Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient, Preprint MS-01-06, School of Mathematical Sciences, Dublin City University (2001)

    Google Scholar 

  6. Lazarov, R.D., Michev, I.D., Vassilevski, P.S.: Finite volume methods for convection- diffusion problems. SIAM J. Numer. Anal. 33(1), 31–55 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Linss, T.: Finite difference schemes for convection-diffusion problems with a concentrated source and discontinuous convection field. Computational Methods in Applied Mathematics 2(1), 41–49 (2002)

    MATH  MathSciNet  Google Scholar 

  8. Linss, T.: Uniform pointwise convergence of an upwind finite volume method on layer-adapted meshes. ZAMM 82(4), 247–254 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Fitted numerical methods for singular perturbation problems. World Scientific, Singapore (1996)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center of Applied Mathematics and Informatics, University of Rousse, 7017, Rousse, Bulgaria

    Iliya A. Brayanov & Lubin G. Vulkov

Authors
  1. Iliya A. Brayanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lubin G. Vulkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

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

    Jerzy Waśniewski

  4. Center of Applied Mathematics and Informatics, University of Rousse, 7017, Rousse, Bulgaria

    Plamen Yalamov

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brayanov, I.A., Vulkov, L.G. (2004). Finite Volume Difference Methods for Convection-Dominated Problems with Interface. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24588-9_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21090-0

  • Online ISBN: 978-3-540-24588-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation