### 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 language | English (US) |
---|---|

Pages (from-to) | 1097-1120 |

Number of pages | 24 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 23 |

Issue number | 6 |

State | Published - Dec 1986 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*23*(6), 1097-1120.

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

Research output: Contribution to journal › Article

*SIAM Journal on Numerical Analysis*, vol. 23, no. 6, pp. 1097-1120.

}

TY - JOUR

T1 - ITERATIVE METHODS FOR THE SOLUTION OF ELLIPTIC PROBLEMS ON REGIONS PARTITIONED INTO SUBSTRUCTURES.

AU - Bjorstad, Petter E.

AU - Widlund, Olof B.

PY - 1986/12

Y1 - 1986/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022918065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022918065&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 1097

EP - 1120

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 6

ER -