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

摘要

A semidiscrete finite volume element ( FVE) approximation to a parabolic integrodifferential equation ( PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimalorder L-2-error estimate for smooth initial data and nearly the same optimal-order L-2-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(-1)h(2) ln h) in the L-2-norm for positive time when the given initial function is only in L-2.