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A Note on the Optimal L 2-Estimate of the Finite Volume Element Method

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Abstract

In this note, the optimal L 2-error estimate of the finite volume element method (FVE) for elliptic boundary value problem is discussed. It is shown that ‖u−u h ‖0≤Ch 2|ln h|1/2‖f‖1,1 and ‖u−u h ‖0≤Ch 2‖f‖1,p , p>1, where u is the solution of the variational problem of the second order elliptic partial differential equation, u h is the solution of the FVE scheme for solving the problem, and f is the given function in the right-hand side of the equation.

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Authors and Affiliations

  1. Department of Scientific Computation, Zhongshan University, Guangzhou, 510275, P.R. China

    Zhongying Chen

  2. Department of Mathematics, Jilin University, Changchun, 130023, P.R. China

    Ronghua Li

  3. Institute of Computational Mathematics, and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, China

    Aihui Zhou

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  1. Zhongying Chen
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  2. Ronghua Li
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  3. Aihui Zhou
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Chen, Z., Li, R. & Zhou, A. A Note on the Optimal L 2-Estimate of the Finite Volume Element Method. Advances in Computational Mathematics 16, 291–303 (2002). https://doi.org/10.1023/A:1014577215948

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