Non-classical H ¹ projection and Galerkin methods for non-linear parabolic integro-differential equations

In this paper the Galerkin method is analyzed for the following nonlinear integro-differential equation of parabolic type: {Mathematical expression} Optimal L 2 error estimates for Crank-Nicolson and extrapolated Crank-Nicolson approximations are derived by using a non-classical H 1 projection associated with the above equation. Both schemes result in procedures which are second order correct in time, but the latter requires the solution of a linear algebraic system only once per time step.