### Abstract

A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.

Original language | English (US) |
---|---|

Pages (from-to) | 881-909 |

Number of pages | 29 |

Journal | Mathematics of Computation |

Volume | 69 |

Issue number | 231 |

State | Published - Jul 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*69*(231), 881-909.

}

*Mathematics of Computation*, vol. 69, no. 231, pp. 881-909.

**Local and parallel finite element algorithms based on two-grid discretizations.** / Xu, Jinchao; Zhou, Aihui.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Local and parallel finite element algorithms based on two-grid discretizations

AU - Xu, Jinchao

AU - Zhou, Aihui

PY - 2000/7/1

Y1 - 2000/7/1

N2 - A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.

AB - A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.

UR - http://www.scopus.com/inward/record.url?scp=0040735802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040735802&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040735802

VL - 69

SP - 881

EP - 909

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 231

ER -