ITERATIVE METHODS FOR THE SOLUTION OF ELLIPTIC PROBLEMS ON REGIONS PARTITIONED INTO SUBSTRUCTURES.

Petter E. Bjorstad, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Finite element problems can often naturally be divided into subproblems which correspond to subregions into which the region has been partitioned or from which it was originally assembled. A class of iterative methods is discussed in which these subproblems are solved by direct methods, while the interaction across the curves or surfaces which divide the region is handled by a conjugate gradient method. A mathematical framework for this work is provided by regularity theory for elliptic finite element problems and by block Gaussian elimination. A full development of the theory, which shows that certain of these methods are optimal, is given for Lagrangian finite element approximations of second order linear elliptic problems in the plane. Results from numerical experiments are also reported.

Original languageEnglish (US)
Pages (from-to)1097-1120
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume23
Issue number6
StatePublished - Dec 1986

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Conjugate gradient method
Substructure
Iterative methods
Elliptic Problems
Finite Element
Iteration
Regularity Theory
Gaussian elimination
Conjugate Gradient Method
Finite Element Approximation
Direct Method
Divides
Experiments
Numerical Experiment
Curve
Interaction
Class
Framework

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

ITERATIVE METHODS FOR THE SOLUTION OF ELLIPTIC PROBLEMS ON REGIONS PARTITIONED INTO SUBSTRUCTURES. / Bjorstad, Petter E.; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 23, No. 6, 12.1986, p. 1097-1120.

Research output: Contribution to journalArticle

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