Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems

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^∞ (0,T; L² (Ω)). 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.