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Numerische Mathematik

, Volume 50, Issue 4, pp 451–475 | Cite as

Finite element solution of nonlinear elliptic problems

  • Miloslav Feistauer
  • Alexander Ženíšek
Convergence of the SSOR Method for Nonlinear Systems of Simultaneous Equations

Summary

The study of the finite element approximation to nonlinear second order elliptic boundary value problems with mixed Dirichlet-Neumann boundary conditions is presented. In the discretization variational crimes are commited (approximation of the given domain by a polygonal one, numerical integration). With the assumption that the corresponding operator is strongly monotone and Lipschitz-continuous and that the exact solutionuH1(Ω), the convergence of the method is proved; under the additional assumptionuH2(Ω), the rate of convergenceO(h) is derived without the use of Green's theorem.

Subject Classifications

AMS(MOS) 65N30 CR: G1.8 

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Miloslav Feistauer
    • 1
  • Alexander Ženíšek
    • 2
  1. 1.Charles University PraguePraha 8Czechoslovakia
  2. 2.Technical University BrnoBrnoCzechoslovakia

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