The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems
نویسندگان
چکیده
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: max P∈S |(∇u−∇uh)(P)| = O(h2)| lnh|, where ∇uh(P) 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 elements.
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