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

Jinchao Xu, Aihui Zhou

Research output: Contribution to journalArticle

136 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)881-909
Number of pages29
JournalMathematics of Computation
Volume69
Issue number231
StatePublished - Jul 1 2000

Fingerprint

Discretization
Finite Element
Grid
Boundary value problems
A Posteriori Estimates
Adaptive Finite Elements
Finite Element Solution
Elliptic Boundary Value Problems
Elliptic Problems
Low Frequency
Numerical Experiment
Experiments
Observation

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{0a47d4147e254ae5971197704ba65239,
title = "Local and parallel finite element algorithms based on two-grid discretizations",
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.",
author = "Jinchao Xu and Aihui Zhou",
year = "2000",
month = "7",
day = "1",
language = "English (US)",
volume = "69",
pages = "881--909",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
number = "231",

}

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

In: Mathematics of Computation, Vol. 69, No. 231, 01.07.2000, p. 881-909.

Research output: Contribution to journalArticle

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 -