Skip to main content
SpringerLink
Log in

Numerical results and error estimates for the finite element solution of problems with nonlinear boundary condition on nonpolygonal domains

  • Conference paper
Numerical Mathematics and Advanced Applications

  • 1177 Accesses

Summary

Problems with nonlinear boundary condition are studied on an elliptic 2nd order problem with nonlinear Newton boundary condition in a bounded two-dimensional domain. The main attention is paid to the analysis of the the error estimates. The effect of numerical integration is included. The obtained theoretical error estimates are documented on several numerical examples.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ciarlet, P.G. (1978): The finite element method for elliptic problems. North Holland, Amsterdam

    MATH  Google Scholar 

  2. Feistauer, M., Kalis, H., Rokyta, M. (1989): Mathematical modelling of an electrolysis process. Comment Math. Univ. Carolin. 30, 465–477

    MathSciNet  MATH  Google Scholar 

  3. Feistauer, M., Najzar, K. (1998): Finite element approximation of a problem with a nonlinear Newton boundary condition. Numer. Math. 78, 403–425

    Article  MathSciNet  MATH  Google Scholar 

  4. Feistauer, M., Najzar, K., Sobotíková, V. (1999): Error estimates for the finite element solution of elliptic problems with nonlinear Newton boundary conditions. Numer. Funct. Anal. Optim. 20, 835–851

    Article  MathSciNet  MATH  Google Scholar 

  5. Feistauer, M., Najzar, K., Sobotíková, V. (2001): On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains. Appl. Math. 46, 353–382

    Article  MathSciNet  MATH  Google Scholar 

  6. Feistauer, M., Najzar, K., Sobotíková, V., Sváček, P. (2000): Numerical analysis of problems with nonlinear Newton boundary conditions. In: Neittaanmäki, P. et al. (eds.): ENUMATH 99. World Scientific, Singapore. pp. 486–493

    Google Scholar 

  7. Nečas, J. (1967): Les méthodes directes en théories des équations elliptiques. Academia, Prague

    Google Scholar 

  8. Sváček, P. (1999): Higher order finite element method for a problem with nonlinear boundary condition. In: Proceedings of the 13th summer school “Software and Algorithms of Numerical Mathematics”. West Bohemian University, Pilsen

    Google Scholar 

  9. Sváček, P., Najzar, K. (2002): Numerical solution of problems with non-linear boundary conditions. Math. Comput. Simulation, to appear. DOI: 10.1016/S0378-4754(02)000782

    Google Scholar 

  10. Ženíšek, A. (1981): Nonhomogeneous boundary conditions and curved triangular finite elements. Appl. Math. 26, 121–141

    MATH  Google Scholar 

  11. Zlámal, M. (1973): Curved elements in the finite element method. I. SIAM J. Numer. Anal. 10, 229–240

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engeneering, Czech Technical University, Praha, Czech Republic

    P. Sváček

  2. Department of Numerical Analysis, Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    K. Najzar

Authors
  1. P. Sváček
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Najzar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. e Tecnologie Informatiche IMATI-CNR, Università di Pavia and Istituto di Matematica Applicata, Pavia, Italy

    Franco Brezzi

  2. e Tecnologie Informatiche IMATI-CNR, Istituto di Matematica Applicata, Pavia, Italy

    Annalisa Buffa

  3. e Reti ad Alte Prestazioni ICAR-CNR, Istituto per il Calcolo, Napoli, Italy

    Stefania Corsaro

  4. e Reti ad Alte Prestazioni ICAR-CNR, Università di Napoli and Istituto per il Calcolo, Napoli, Italy

    Almerico Murli

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Italia

About this paper

Cite this paper

Sváček, P., Najzar, K. (2003). Numerical results and error estimates for the finite element solution of problems with nonlinear boundary condition on nonpolygonal domains. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_56

Download citation

  • DOI: https://doi.org/10.1007/978-88-470-2089-4_56

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-2167-9

  • Online ISBN: 978-88-470-2089-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation