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

中文翻译：

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从一维有限体积元方法开发的新超收敛结构

有限体积元法（FVEM）引入了新的超收敛结构，允许我们自由选择超收敛点。建立一般正交条件和改进的M-分解(MMD)技术来证明新结构的超收敛特性。此外，正交条件与FVE方案的收敛特性之间的关系如表1所示。给出了数值结果来说明理论结果。