Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation

In this paper, the error analysis of a two-grid method (TGM) with backward Euler scheme is discussed for semilinear parabolic equation. Contrary to the conventional finite element analysis, the error between exact solution and finite element solution is split into two parts (temporal error and spatial error) by introducing a corresponding time-discrete system. This can lead to the spatial error independent of τ (time step). Secondly, based on the above technique, optimal error estimates in L2 and H1-norms of TGM solution are deduced unconditionally, while previous works always require a certain time step size condition. Finally, a numerical experiment is provided to confirm the theoretical analysis.