Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data

Abstract. A semidiscrete finite volume element (FVE) approximation to a parabolic integrodifferential equation (PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimalorder L2-error estimate for smooth initial data and nearly the same optimal-order L2-error estimate for nonsmooth initial data are obtained. More precisely, for homogeneous equations, an elementary energy technique and a duality argument are used to derive an error estimate of order O ( t−1h2 lnh )