本项目拟针对超材料中复杂Maxwell方程数学模型，研究其棱有限元离散及其超收敛现象、棱有限元重构技术、基于重构的后验误差估计理论与自适应棱有限元方法。获得棱有限元的超逼近/超收敛结果，设计棱有限元的超收敛重构方法，构造棱有限元基于重构技术的后验误差估计，设计网格加密和粗化、移动相结合的网格自适应策略，将超收敛、重构技术、后验误差估计、自适应有机结合，发展一套高效的自适应棱有限元方法，模拟电磁波在超材料中的传播，并建立相关数学理论。

The project is concerned with the numerical method for the Maxwell equations in the metamaterials. The research topics are including the edge finite element methods and it superconvergence analysis, recovery techniques of edge finite element, recovery based a posteriori error estimation and adaptive edge finite element methods. We plan to study the superclose/superconvergence results for edge finite element methods，develop superconvergent recovery methods and construct recovery type a posteriori error estimators for edge finite element methods, integrate mesh refining, coarsening and moving to design the mesh adaptive strategy. The goal of this project is to integrate the superconvergence and recovery techniques, a posteriori error estimations in the mesh adaptivity, to develop an efficient adaptive edge finite element method for simulating the propagation of electromagnetic wave in metamaterials, and establish their mathematical theories.