Numerische Mathematik

, Volume 58, Issue 1, pp 51–77 | Cite as

The finite element method for nonlinear elliptic equations with discontinuous coefficients

  • Alexander Ženíšek


The study of the finite element approximation to nonlinear second order elliptic boundary value problems with discontinuous coefficients is presented in the case of mixed Dirichlet-Neumann boundary conditions. The change in domain and numerical integration are taken into account. With the assumptions which guarantee that the corresponding operator is strongly monotone and Lipschitz-continuous the following convergence results are proved: 1. the rate of convergenceO(hε) if the exact solutionuH1 (Ω) is piecewise of classH1+ε (0<ε≦1);2. the convergence without any rate of convergence ifuH1 (Ω) only.

Subject classifications

AMS(MOS) 65N30 CR G1.8 


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Alexander Ženíšek
    • 1
  1. 1.Department of MathematicsTechnical University BrnoBrnoCzechoslovakia

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