ON SUPERCONVERGENCE RESULTS
AND NEGATIVE NORM ESTIMATES FOR
PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

AMIYA K. PANI AND RAJEN K. SINHA

Abstract:

The purpose of this paper is to show how known negative norm estimates and superconvergence results applied to parabolic equations can be carried over to integro-differential equations of parabolic type. A quasi projection technique introduced earlier by Douglas, Dupont and Wheeler is modified to establish negative norm estimates in several space variables. Further, in a single space variable, knot superconvergence is also established. Finally, interior superconvergence estimates are also derived.