Local superconvergence properties of the post-processed finite volume element method (FVEM) are studied. Some interpolation/extrapolation post-processing techniques are applied to a class of k th-order (k ≥ 2) FVE solutions for elliptic equations. A local analysis tool for the finite volume method is developed to analyze the proposed method, and some superconvergence results are established. The theoretical findings are supported by several numerical experiments.

中文翻译：

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后处理高阶有限体积单元解的局部超收敛

研究了后处理有限体积元方法（FVEM）的局部超收敛特性。一些内插/外插后处理技术被应用于一类的ķ阶（ķ ≥2）为椭圆方程FVE解决方案。开发了一种用于有限体积方法的局部分析工具来分析该方法，并建立了一些超收敛结果。理论发现得到了一些数值实验的支持。