In this paper, we study the unconditional convergence and error estimates of a two-grid finite element method for the semilinear parabolic integro-differential equations. By using a temporal-spatial error splitting technique, optimal
$$L^p$$
and
$$H^1$$
error estimates of the finite element method can be obtained. Moreover, to deal with the semilinearity of the model, we use the two-grid method. Optimal error estimates in
$$L^2$$
and
$$H^1$$
-norms of two-grid solution are derived without any time-step size conditions. Finally, some numerical results...
