Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data
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A semidiscrete finite volume element (FVE) approximation to a parabolic integro-differential equation (PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimal-order 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. © 2006 Society for Industrial and Applied Mathematics.
author list (cited authors)
Sinha, R. K., Ewing, R. E., & Lazarov, R. D.