SUPERCONVERGENCE OF MIXED FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS WITH NONSMOOTH INITIAL DATA

A semidiscrete mixed finite element approximation to parabolic initial -boundary value problems is introduced and analyzed. Superconvergence estimates for both pressure and velocity are obtained. The estimates f or 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 sufficiently large. Because of the smoothing properties of the parabolic operator, these estimates for large time levels essentia lly coincide with the estimates obtained earlier for smooth solutions. However, for small time intervals we obtain the correct convergence o rders for nonsmooth data.