| Abstract: | A two-grid finite element approximation is studied in the fully discretescheme obtained by discretizing in both space and time for a nonlinear hyperbolicequation. The main idea of two-grid methods is to use a coarse-grid space ($S_H$) toproduce a rough approximation for the solution of nonlinear hyperbolic problemsand then use it as the initial guess on the fine-grid space ($S_h$). Error estimates arepresented in $H^1$-norm, which show that two-grid methods can achieve the optimalconvergence order as long as the two different girds satisfy $h$ = $mathcal{O}$($H^2$). With theproposed techniques, we can obtain the same accuracy as standard finite elementmethods, and also save lots of time in calculation. Theoretical analyses and numerical examples are presented to confirm the methods. |
