Skip to main content
SpringerLink
Log in

Exponential Decay to Equilibrium of Nonlinear DDFV Schemes for Convection-Diffusion Equations

  • Conference paper
  • First Online:
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (FVCA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 323))

Included in the following conference series:

  • 1087 Accesses

Abstract

We introduce a nonlinear DDFV scheme for an anisotropic linear convec tion-diffusion equation with mixed boundary conditions and we establish the exponential decay of the scheme towards its steady-state.

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

Access this chapter

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Andreianov, B., Boyer, F., Hubert, F.: Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Numer. Methods Part. Differ. Equ. 23(1), 145–195 (2007)

    Article  MathSciNet  Google Scholar 

  2. Bodineau, T., Lebowitz, J., Mouhot, C., Villani, C.: Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations. Nonlinearity 27, 2111–2132 (2014)

    Article  MathSciNet  Google Scholar 

  3. Cancès, C., Chainais-Hillairet, C., Krell, S.: Numerical analysis of a nonlinear free-energy diminishing discrete duality finite volume scheme for convection diffusion equations. Comput. Methods Appl. Math. 18, 407–432 (2018)

    Article  MathSciNet  Google Scholar 

  4. Chainais-Hillairet, C., Herda, M.: Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations. IMAJNA (2019)

    Google Scholar 

  5. Cancès, C., Chainais-Hillairet, C., Herda, M., Krell, S.: Large time behavior of nonlinear finite volume schemes for convection-diffusion equations. https://hal.archives-ouvertes.fr/hal-02360155 (2019)

Download references

Author information

Authors and Affiliations

  1. Univ. Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé, 59000, Lille, France

    Claire Chainais-Hillairet

  2. Université Côte d’Azur, CNRS, Inria, LJAD, Nice, France

    Stella Krell

Authors
  1. Claire Chainais-Hillairet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stella Krell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stella Krell .

Editor information

Editors and Affiliations

  1. NORCE Norwegian Research Centre AS, Bergen, Norway

    Robert Klöfkorn

  2. Department of Mathematics, University of Bergen, Bergen, Norway

    Eirik Keilegavlen

  3. Department of Mathematics, University of Bergen, Bergen, Norway

    Florin A. Radu

  4. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chainais-Hillairet, C., Krell, S. (2020). Exponential Decay to Equilibrium of Nonlinear DDFV Schemes for Convection-Diffusion Equations. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_11

Download citation

Publish with us

Policies and ethics

Search

Navigation