@article {Carson_2017_ErrorEstimation,
	title = {Analysis of output-based error estimation for finite element methods},
	journal = {Applied Numerical Mathematics},
	volume = {118},
	year = {2017},
	pages = {182 - 202},
	abstract = {Abstract In this paper, we develop a priori estimates for the convergence of outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Output error estimates for order p finite element solutions are constructed using the Dual-Weighted Residual (DWR) method with a higher-order p ' \&gt; p dual solution. Specifically, we analyze these \{DWR\} estimates for Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized \{DG\} (HDG) methods applied to the Poisson problem. For all discretizations, as h {\textrightarrow} 0 , we prove that the output and output error estimate converge at order 2p and 2 p ' (assuming sufficient smoothness), while localizations of the output and output error estimate converge at 2 p + d and p + p ' + d . For DG, the results use a new post processing for the error associated with the lifting operator. For HDG, these rates improve an additional order when the stabilization is based upon an O ( 1 ) length scale.},
	keywords = {Hybridizable Discontinuous Galerkin},
	issn = {0168-9274},
	doi = {http://dx.doi.org/10.1016/j.apnum.2017.03.004},
	url = {http://www.sciencedirect.com/science/article/pii/S0168927417300648},
	author = {Carson, H A and Darmofal, D L and Galbraith, M C and Allmaras, S R}
}
