SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1885-A1912, January 2020.
This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds which have been assumed for some significant gradient recovery methods in the literature. Another advantage of PPPR is that superconvergence is guaranteed without the symmetric condition which is required in the existing techniques. As an application, we show its capability of constructing an asymptotically exact a posteriori error estimator. Several numerical examples on two-dimensional surfaces are presented to support the theoretical results, and comparisons with existing methods are documented, showing that PPPR outperforms the other methods, in particular in the case of high curvature surfaces as well as mildly structured meshes.

中文翻译：

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流形上的参数多项式保留恢复

SIAM科学计算杂志，第42卷，第3期，第A1885-A1912页，2020年1月。
本文研究了离散流形上定义的数据的梯度恢复方案。所提出的方法，参数多项式保留恢复（PPPR），不需要精确流形的切线空间，而这些流形已在文献中针对某些重要的梯度恢复方法进行了假设。PPPR的另一个优点是，在没有现有技术要求的对称条件的情况下，可以保证超收敛。作为一个应用，我们展示了它构造渐近精确的后验误差估计量的能力。给出了二维表面上的几个数值示例以支持理论结果，并记录了与现有方法的比较，表明PPPR优于其他方法，