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Analysis of stabilized finite volume method for poisson equation

    Tong Zhang Affiliation
    ; Pengzhan Huang Affiliation
    ; Shunwei Xu Affiliation

Abstract

In this work, we systematically analyze a stabilized finite volume method for the Poisson equation. On stating the convergence of this method, optimal error estimates in different norms are obtained by establishing the adequate connections between the finite element and finite volume methods. Furthermore, some super-convergence results are established by using L 2 -projection method on a coarse mesh based on some regularity assumptions for Poisson equation. Finally, some numerical experiments are presented to confirm the theoretical findings.

Keyword : Poisson equation, finite volume method, projection method, superconvergence

How to Cite
Zhang, T., Huang, P., & Xu, S. (2013). Analysis of stabilized finite volume method for poisson equation. Mathematical Modelling and Analysis, 18(3), 415-431. https://doi.org/10.3846/13926292.2013.805172
Published in Issue
Jun 1, 2013
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This work is licensed under a Creative Commons Attribution 4.0 International License.