A two-gird method for finite element solution of parabolic integro-differential equations

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 are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.