Error Estimates of the Classical and Improved Two-Grid Methods (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we obtain the first error estimate in $L^2$-norm for the classicaltwo-grid method, then design an improved two-grid method by adding one morecorrection on the coarse space to the classical two-gird method. Furthermore, we alsopresent the error estimates in both $L^2$-norm and $H^1$-norm for the improved two-gridmethod. Especially, the $L^2$ error estimate of the improved two-grid method is one orderhigher than that of the classical two-grid. At last, we confirm and illustrate thetheoretical result by some numerical experiments.