Numerische Mathematik

, Volume 35, Issue 3, pp 277–291 | Cite as

On the efficient solution of nonlinear finite element equations I

  • Hans Detlef Mittelmann
Sign-Stability in Difference Schemes for Parabolic Initinal-Boundary Value Problems


On the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of elliptic boundary value problems. A simplified relaxation algorithm which needs no information about the Jacobian of the system is combined with a correspondingly modified conjugate gradient method. A global convergence proof is given and the number of operations required is compared with that of other algorithms which are equally applicable to a large class of problems. Numerical results verify the efficiency for some typical examples.

Subject Classifications

AMS(MOS) 65N30 65H10 65K10 CR: 5.17, 5.15 


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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Hans Detlef Mittelmann
    • 1
  1. 1.Abteilung Mathematik der Universität DortmundDortmund 50Germany (Fed. Rep.)

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