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Numerische Mathematik

, Volume 58, Issue 1, pp 713–735 | Cite as

On the finite volume element method

  • Zhiqiang Cai
Article

Summary

The finite volume element method (FVE) is a discretization technique for partial differential equations. It uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations, then restricts the admissible functions to a finite element space to discretize the solution. this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with FVE based on triangulations with linear finite element spaces and a general type of control volume. We establishO(h) estimates of the error in a discreteH1 semi-norm. Under an additional assumption of local uniformity of the triangulation the estimate is improved toO(h2). Results on the effects of numerical integration are also included.

Subject classifications

AMS(MOS): 65N10 65N30 CR: G1.8 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Zhiqiang Cai
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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