Sobolev space preconditioning for Newton's method using domain decomposition

O. Axelsson, I. Faragó, J. Karátson

Research output: Contribution to journalArticle

10 Citations (Scopus)


An inner-outer iteration is constructed for ill-conditioned non-linear elliptic boundary value problems, using a damped inexact Newton Method for the outer and a conjugate gradient method for the inner iteration. The focus is on efficient preconditioning for the inner iteration. Sobolev space background is used to construct preconditioners as discretizations of appropriately chosen piecewise constant coefficient elliptic operators. The combination of this theoretical approach with a suitable domain decomposition idea results in well-structured preconditioners that are able to compensate for the sharp gradients of the coefficients. Furthermore, convergence estimates and mesh independence of the condition numbers are direct consequences of the method.

Original languageEnglish
Pages (from-to)585-598
Number of pages14
JournalNumerical Linear Algebra with Applications
Issue number6-7
Publication statusPublished - Jan 1 2002



  • Newton's method
  • Preconditioning
  • Sobolev space background

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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