Maxwell方程数值求解的高效计算方法研究，在科学计算和工程计算领域占有重要位置，受到越来越多的重视。基于后验误差估计的自适应算法可以大大提高计算效率，节省计算资源，而重构技术在后验误差估计中占有重要地位。Maxwell方程有限元重构技术的相关工作还比较少见，集中研究Maxwell方程的有限元重构技术、后验误差估计及自适应有限元方法具有非常重要的意义。本项目拟研究棱单元的curl重构技术，包括超收敛片梯度重构（SPR）、多项式保持重构（PPR）和超收敛点团重构（SCR），建立基于重构的超收敛分析和渐近精确的后验误差估计，证明后验误差估计的有效性和可靠性。在此基础上，研制电磁场的三维自适应有限元程序，通过典型算例验证重构技术的有效性和自适应方法的最优性，项目成果将为电磁场计算提供一种更高效的计算方法。

The study of the efficient computing method for numerically solving the Maxwell equations, plays an important part in the field of scientific computation and engineering computation, and attracts more and more attention. Adaptive algorithm based on a posteriori error estimation can greatly improve computing efficiency and save computing resources, while recovery technique plays an important role in a posteriori error estimation. The finite element recovery technique for Maxwell equations is relatively rare. It is very important to concentrate on the finite element recovery technique, a posteriori error estimation and adaptive finite element method for Maxwell equations. This project aims to study the curl recovery of the edge element, including Superconvergent Patch Recovery (SPR), Polynomial Preserving Recovery (PPR) and Superconvergent Cluster Recovery (SCR), establishes superconvergence analysis and asymptotically accurate a posteriori error estimation based on recovery, and proves the effectiveness and reliablility of the error estimator. Meanwhile, we will develop a three-dimensional adaptive finite element program of electromagnetic field. The effectiveness of the recovery technique and the optimality of the adaptive method are verified by typical numerical examples. The project results will provide a more efficient computing method for electromagnetic field calculation.