On superconvergence results and negative norm estimates for parabolic integro-differential equations

Abstract

The purpose of this paper is to show howknown negative norm estimates and superconvergence resultsapplied to parabolic equations can be carried over to integro-differential equations of parabolic type. A quasi projectiontechnique introduced earlier by Douglas, Dupont and Wheeleris modified to establish negative norm estimates in severalspace variables. Further, in a single space variable, knot su-perconvergence is also established. Finally, interior supercon-vergence estimates are also derived.