Elliptic reconstruction and a posteriori error estimates for parabolic problems

摘要

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-infinity(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. [References: 27]