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New superconvergent structures are introduced by the finite volume elementmethod (FVEM), which allow us to choose the superconvergent points freely. Thegeneral orthogonal condition and the modified M-decomposition (MMD) techniqueare established to prove the superconvergence properties of the new structures.In addition, the relationships between the orthogonal condition and theconvergence properties for the FVE schemes are carried out in Table 1.Numerical results are given to illustrate the theoretical results.

New superconvergent structures developed from the finite volume element method in 1D