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The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

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


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: (T. Zhang), (L.-X. Tang)


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The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

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


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