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The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

  • Tie Zhang (a1) and Lixin Tang (a1)
Abstract
Abstract

We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property:

where denotes the average gradient on elements containing point P and S is the set of optimal stress points composed of the mesh points, the midpoints of edges and the centers of elements.

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*Corresponding author. Email addresses: ztmath@163.com (T. Zhang), lixintang@mail.neu.edu.cn (L.-X. Tang)
References
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Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
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