(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we obtain the first error estimate in L^2-norm for the classical two-grid method, then design an improved two-grid method by adding one more correction on the coarse space to the classical two-gird method. Furthermore, we also present the error estimates in both L^2-norm and H^1-norm for the improved two-grid method. Especially, the L^2 error estimate of the improved two-grid method is one order higher than that of the classical two-grid. At last, we confirm and illustrate the theoretical result by some numerical experiments.