Numerische Mathematik Manuscript-nr. Superconvergence of Mixed Nite Element Methods for Parabolic Problems with Nonsmooth Initial Data

A semidiscrete mixed nite element approximation to parabolic initial-boundary value problems is introduced and analyzed. Superconvergence estimates for both pressure and velocity are obtained. The estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in L 2 and data in H r , for r suuciently large. Because of the smoothing properties of the parabolic operator, these estimates for large time levels essentially coincide with the estimates obtained earlier for smooth solutions. However, for small time intervals we obtain the correct convergence orders for nonsmooth data.