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

  • P. Sváček
  • K. Najzar
Conference paper


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.


Quadrature Formula Convergence Order Finite Element Solution Nonlinear Boundary Condition Polygonal Domain 
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  1. [1]
    Ciarlet, P.G. (1978): The finite element method for elliptic problems. North Holland, AmsterdamMATHGoogle Scholar
  2. [2]
    Feistauer, M., Kalis, H., Rokyta, M. (1989): Mathematical modelling of an electrolysis process. Comment Math. Univ. Carolin. 30, 465–477MathSciNetMATHGoogle Scholar
  3. [3]
    Feistauer, M., Najzar, K. (1998): Finite element approximation of a problem with a nonlinear Newton boundary condition. Numer. Math. 78, 403–425MathSciNetMATHCrossRefGoogle Scholar
  4. [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, 835–851MathSciNetMATHCrossRefGoogle Scholar
  5. [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, 353–382MathSciNetMATHCrossRefGoogle Scholar
  6. [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. 486–493Google Scholar
  7. [7]
    Nečas, J. (1967): Les méthodes directes en théories des équations elliptiques. Academia, PragueGoogle Scholar
  8. [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, PilsenGoogle Scholar
  9. [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)000782Google Scholar
  10. [10]
    Ženíšek, A. (1981): Nonhomogeneous boundary conditions and curved triangular finite elements. Appl. Math. 26, 121–141MATHGoogle Scholar
  11. [11]
    Zlámal, M. (1973): Curved elements in the finite element method. I. SIAM J. Numer. Anal. 10, 229–240MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • P. Sváček
    • 1
  • K. Najzar
    • 2
  1. 1.Department of Technical Mathematics, Faculty of Mechanical EngeneeringCzech Technical UniversityPrahaCzech Republic
  2. 2.Department of Numerical Analysis, Faculty of Mathematics and PhysicsCharles UniversityPrahaCzech Republic

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