On the efficient solution of nonlinear finite element equations I

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)277-291
Number of pages15
JournalNumerische Mathematik
Volume35
Issue number3
DOIs
StatePublished - Sep 1 1980
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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