A posteriori finite element bounds for output functionals of discontinuousGalerkin discretizations of parabolic problems

We present a Neumann-subproblem a posteriori finite element procedure for t he efficient calculation of constant-free. sharp lower and upper estimators for linear functional outputs or parabolic equations discretized by a disc ontinuous Galerkin method in time. In space, a global coarse mesh and a dec oupled line mesh are used to compute the estimators which are shown to conv erge to the value of the output obtained fur a global coupled fine mesh. We first formulate the bound procedure, with particular emphasis on the proof of the: bounding properties. We then provide an illustrative numerical exa mple: a problem of heat conduction in a composite material. (C) 2001 Elsevi er Science B.V. All rights reserved.