Optimal error estimates of Galerkin method for a nonlinear parabolic integro-differential equation

In this paper, the error analysis of Galerkin finite element method (FEM) is investigated for a nonlinear parabolic integro-differential equation in two dimensions. By skillfully and rigorously manipulating the nonlinear term, optimal error estimates in L-infinity (L-2(Omega)) and L-infinity (H-1(Omega)) are obtained for a linearized backward Euler fully-discrete scheme, which improves the suboptimal approximation in L-infinity (L-2(Omega)) in the previous literature. Finally, some numerical results are provided to verify the theoretical findings. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.