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Advances in Computational Mathematics

, Volume 5, Issue 1, pp 15–29 | Cite as

The analysis of multigrid algorithms for cell centered finite difference methods

  • James H. Bramble
  • Richard E. Ewing
  • Joseph E. Pasciak
  • Jian Shen
Article

Abstract

In this paper, we examine multigrid algorithms for cell centered finite difference approximations of second order elliptic boundary value problems. The cell centered application gives rise to one of the simplest non-variational multigrid algorithms. We shall provide an analysis which guarantees that the W-cycle and variable V-cycle multigrid algorithms converge with a rate of iterative convergence which can be bounded independently of the number of multilevel spaces. In contrast, the natural variational multigrid algorithm converges much more slowly.

AMS subject classification

Primary 65N30 Secondary 65F10 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • James H. Bramble
    • 1
  • Richard E. Ewing
    • 1
  • Joseph E. Pasciak
    • 2
  • Jian Shen
    • 3
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of Applied ScienceBrookhaven National LaboratoryUptonUSA
  3. 3.Institute for Scientific ComputationTexas A&M UniversityCollege StationUSA

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