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An Unconditionally Stable Quadratic Finite Volume Scheme over Triangular Meshes for Elliptic Equations

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Abstract

In this note, we present and analyze a special quadratic finite volume scheme over triangular meshes for elliptic equations. The scheme is designed with the second degree Gauss points on the edges and the barycenters of the triangle elements. With a novel from-the-trial-to-test-space mapping, the inf–sup condition of the scheme is shown to hold independently of the minimal angle of the underlying mesh. As a direct consequence, the \(H^1\) norm error of the finite volume solution is shown to converge with the optimal order.

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Acknowledgments

The author is indebted to Dr. Hailong Guo of Wayne State University for the figures designed in the paper.

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Authors and Affiliations

  1. School of Data and Computer Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China

    Qingsong Zou

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  1. Qingsong Zou
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Correspondence to Qingsong Zou.

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Supported in part by the National Natural Science Foundation of China through the Grants 11571384, 11171359 and 11428103, in part by Guangdong Provincial Natural Science Foundation of China through the grant 2014A030313179, and in part by the Fundamental Research Funds for the Central Universities of China through the grant 16lgjc80.

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Zou, Q. An Unconditionally Stable Quadratic Finite Volume Scheme over Triangular Meshes for Elliptic Equations. J Sci Comput 70, 112–124 (2017). https://doi.org/10.1007/s10915-016-0244-3

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  • DOI: https://doi.org/10.1007/s10915-016-0244-3

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