申请者提出的有限元后处理技巧--保多项式恢复型算子(Polynomial Preserving Recovery)在连续有限元上获得了极大成功，并已被商业软件COMSOL Multiphysics采用。 基于此，本项目计划将该技巧推广到混合间断元(HDG)、拟差分法(MFDM)和弱伽辽金法(WG)等数值方法。分别针对以上各种数值方法，我们计划构造和分析两种保多项式恢复型算法，并对这两种算法的超收敛性给出理论证明和数值验证。

Polynomial Preserving Recovery (PPR), as a post-processing technique for continuous finite element methods proposed by the applicant, turns out to be a big success and thereby, has been adopted by COMSOL Multiphysics, a widely used commerical software. Based upon it, this project is going to generalize the technique to other numerical methods such as Hybridizable Discontinuous Galerkin methods, Mimetic Finite Difference methods, and Weak Galerkin methods. For each of methods aforementioned, two different types of PPR algorithm will be proposed and analyzed. Sound theoretical proof and numerical experiments on superconvergence of these algorithms will be carried out.