“…Compared to the nonlinear Galerkin FE method, the two-grid method can save the CPU time and also get the almost the same errors and convergence rate to the one of nonlinear Galerkin FE method. In view of the advantages of two-grid method, the method has been developed by increasing researchers, the detailed contents can be found in Dawson and Wheeler [6], Chien and Jeng [9], Mu and Xu [8], Wu and Allen [13], Chen et al [10], Chen and Chen [12], Liu et al [14], Chen and Liu [15], Shi and Yang [7], Weng et al [16], Bajpai and Nataraj [18], Zhong et al [28], Liu et al [19], Liu et al [27], Yan et al [30] and some other references. Based on these discussions for two-grid method, ones can see that the time direction is approximated mainly by the second-order Crank-Nicolson (CN) scheme, the second-order two step backward difference (BD) method, and backward Euler (BE) method with first-order convergence rate.…”