## 姚昌辉教授学术报告

In this talk, we design a modified two-grid method (MTGM) for the Maxwell's system by adding one correction on the coarse mesh, called post-processing technique, to the classical two-grid method (TGM),  which makes MTGM run smoothing for the edge element like Lagrange elements. This idea is taken into linear and nonlinear electromagnetic systems ,respectively. Firstly, we give the integral expansion formulas in order to set up supercloseness in the first step of MTGM. Secondly, we take a group of superconvergent solutions on the coarse mesh into the second step as the correction values. Such an algorithm overcomes the difficulties that the edge element can not be applied to the numerical electromagnetic system by TGM directly. Thirdly, we employ the Crank-Nicolson fully discrete scheme to obtain a convergent rate $O(\tau^2+h+H^2)$ for linear systems and $O(\tau^2+h+H^1.5)$  for nonlinear systems by using the lowest mixed $N\acute{e}d\acute{e}lec-Raviart-Thomas$ finite element. In the end, we present three numerical examples to verify our algorithm, which demonstrates that the MTGM can save about 30% CPU time.