Finite element approximation with quadrature to a time dependent parabolic integro-differential equation with nonsmooth initial data

Abstract

In this paper we analyze the effect of numerical quadrature in the finite element analysis for a time dependent parabolicin tegro-differential equation with nonsmooth initial data. Both semi-discrete and fully discrete schemes are discussed and optimal order error estimates are derived in L^∞(L²) and L^∞(H¹) norms using energy method when the initial function is only in H¹₀. Further, quasi-optimal maximum norm estimate is shown to hold for rough initial data.