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The hybrid Wilson finite volume method for elliptic problems on quadrilateral meshes

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Abstract

In this paper, we construct and analyze a nonconforming finite volume method (FVM) for solving the elliptic boundary value problems on quadrilateral meshes: the hybrid Wilson FVM. Under the mesh assumption that the underlying mesh is an h2-parallelogram mesh, we show that the scheme possesses first order in the mesh-dependent H1-norm and second order in the L2-norm error estimates, the same optimal convergence orders as those of the corresponding Wilson finite element method (FEM). Numerical results are presented to demonstrate the theoretical results on the convergence order of the method.

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Funding

This work is supported in part by the National Natural Science Foundation of China under grants 11771375, 11771257, and 11571297, by the Shandong Province Natural Science Foundation under grant ZR2018QA003 and ZR2018MA008.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, People’s Republic of China

    Yuanyuan Zhang, Min Yang & Chuanjun Chen

Authors
  1. Yuanyuan Zhang
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  2. Min Yang
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  3. Chuanjun Chen
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Corresponding author

Correspondence to Yuanyuan Zhang.

Additional information

Communicated by: Paul Houston

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Zhang, Y., Yang, M. & Chen, C. The hybrid Wilson finite volume method for elliptic problems on quadrilateral meshes. Adv Comput Math 45, 429–452 (2019). https://doi.org/10.1007/s10444-018-9623-7

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  • DOI: https://doi.org/10.1007/s10444-018-9623-7

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