A posteriori error estimation of approximate boundary fluxes T. Wildey 1 , S. Tavener 1 , and D. Estep 1, ∗ 1 Department of Mathematics Colorado State University Fort Collins, CO 80523 SUMMARY This paper describes the a posteriori estimation of the error in the flux of a finite element approximation on a piece of the boundary of the domain. The estimate is obtained via a generalized Green’s function corresponding to the quantity of interest on the boundary. We investigate the effects of smoothing the data corresponding to the quantity of interest and explore the effective domain of dependence of the quantity. We relate this approach to previous work by M. F. Wheeler, G. F. Carey, I. Babuska, et al, and M. Larson, et al. Copyright c  2006 John Wiley & Sons, Ltd. key words: a posteriori error estimate, adjoint, boundary flux, effective domain of influence, extraction function, generalized Green’s function, goal-oriented error estimate 1. Introduction Goal-oriented error estimation is critically important in large scale computational science and engineering. Indeed, the situation in which the goal of a computation is to obtain an accurate approximation of a specific quantity of interest, e.g., the normal flux of the solution on a portion of the boundary of the domain, is very common, if not the norm, in practice. Moreover, it is very often possible to compute specific quantities of interest accurately using discretizations that yield poor global accuracy in the sense of some norm. This is critically important in applications that are too complex and large to allow asymptotically resolved discretizations. * Correspondence to: Donald Estep, Department of Mathematics, Colorado State University, Fort Collins, CO 80523, estep@math.colostate.edu Contract/grant sponsor: Department of Energy; contract/grant number: DE-FG02-04ER25620, DE-FG02- 05ER25699 Contract/grant sponsor: National Aeronautics and Space Administration; contract/grant number: NNG04GH63G Contract/grant sponsor: National Science Foundation; contract/grant number: DMS-0107832, DGE- 0221595003, MSPA-CSE-0434354 Contract/grant sponsor: Sandia Corporation; contract/grant number: PO299784