Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to prove the superconvergence of gradient recovery on deviated surfaces. An algorithmic framework for gradient recovery without exact geometric information is introduced. Several numerical examples are documented to validate the theoretical results.

翻译：本文研究了离散曲面上微分结构的超收敛性。新引入的几何超接近性为我们提供了在偏离曲面上证明梯度恢复超收敛性的基本工具。本文介绍了一种无需精确几何信息的梯度恢复算法框架。通过若干数值算例验证了理论结果。