SIAM J. Numer. Anal. (to appear).
Department of Applied Mathematics and Institute of Applied and Computational Mathematics
University of Crete
71409 Heraklion-Crete, Greece
Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA
It is known that the energy technique for a posteriori error analysis of finite element discretizations of parabolic problems yields suboptimal rates in the norm $L^\infty (0,T; L^2 (\Omega)).$ In this paper we combine energy techniques with an appropriate pointwise representation of the error based on an elliptic reconstruction operator which restores the optimal order (and regularity for piecewise polynomials of degree higher than one). This technique may be regarded as the ``dual a posteriori" counterpart of Wheeler's elliptic projection method in the a priori error analysis.