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- W2949279852 abstract "This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove {it 2k-conjecture}: at each vertex of the underlying rectangular mesh, the bi-$k$ degree finite volume solution approximates the exact solution with an order $ O(h^{2k})$, where $h$ is the mesh size. As byproducts, superconvergence properties for finite volume discretization errors at Lobatto and Gauss points are also obtained. All theoretical findings are confirmed by numerical experiments." @default.
- W2949279852 created "2019-06-27" @default.
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- W2949279852 date "2014-01-02" @default.
- W2949279852 modified "2023-09-23" @default.
- W2949279852 title "Is $2k$-Conjecture valid for finite volume methods?" @default.
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- W2949279852 doi "https://doi.org/10.48550/arxiv.1401.0372" @default.
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