A posteriori finite element bounds for output functionals of discontinuous Galerkin discretizations of parabolic problems Original Research Article

We present a Neumann-subproblem a posteriori finite element procedure for the efficient calculation of constant-free, sharp lower and upper estimators for linear functional outputs of parabolic equations discretized by a discontinuous Galerkin method in time. In space, a global coarse mesh and a decoupled fine mesh are used to compute the estimators which are shown to converge to the value of the output obtained for 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 example: a problem of heat conduction in a composite material.