@article {Jayasinghe_2017_Spacetime_Adaptive_Method_Reservoir_Flows_Formulation,
	title = {A space-time adaptive method for reservoir flows: Formulation and one-dimensional application},
	journal = {Computational Geosciences},
	volume = {22},
	year = {2018},
	month = {02/2018},
	pages = {107-123},
	chapter = {107},
	abstract = {<p>This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual-weighted residual method to drive a metric-based mesh optimization algorithm. The space-time adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes.</p>
},
	issn = {1573-1499},
	doi = {10.1007/s10596-017-9673-9},
	url = {http://dx.doi.org/10.1007/s10596-017-9673-9},
	author = {Jayasinghe, Y S and Darmofal, D L and Burgess, N K and Galbraith, M C and Allmaras, S R}
}
@article {Ojeda_2017_AdaptiveCutCellConjugateHT,
	title = {An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of conjugate heat transfer problems},
	journal = {International Journal for Numerical Methods in Engineering},
	volume = {110},
	number = {4},
	year = {2017},
	pages = {350{\textendash}378},
	abstract = {In this paper, we present a solution framework for high-order discretizations of conjugate heat transfer problems on non-body-conforming meshes. The framework consists of and leverages recent developments in discontinuous Galerkin discretization, simplex cut-cell techniques, and anisotropic output-based adaptation. With the cut-cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the discontinuous Galerkin discretization automatically adjusts the mesh in each sub-domain and achieves high-order accuracy in outputs of interest. We demonstrate the solution framework through several multi-domained conjugate heat transfer problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be difficult to capture with user-generated meshes. Copyright {\textcopyright} 2016 John Wiley \& Sons, Ltd.},
	keywords = {adaptation, conjugate heat transfer, cut cells, high-order},
	issn = {1097-0207},
	doi = {10.1002/nme.5362},
	url = {http://dx.doi.org/10.1002/nme.5362},
	author = {Ojeda, S M and Sun, H and Allmaras, S R and Darmofal, D L}
}
@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}
}
@conference {Couchman_2017_FEMweakconvergence,
	title = {On the convergence of higher-order finite element methods to weak solutions},
	booktitle = {AIAA conference paper},
	number = {2017-4274},
	year = {2017},
	keywords = {finite element methods},
	doi = {10.2514/6.2017-4274},
	author = {Couchman, B L and Darmofal, D L and Allmaras, S R and Galbraith, M C}
}
@conference {Zhang_2017_IBL_DG,
	title = {A non-parametric discontinuous Galerkin formulation of the integral boundary layer equations with strong viscous/inviscid coupling},
	booktitle = {AIAA conference paper},
	number = {2017-4278},
	year = {2017},
	keywords = {finite element methods, integral boundary layer methods},
	doi = {10.2514/6.2017-4278},
	author = {Zhang, S and Galbraith, M C and Allmaras, S R and Drela, M and Darmofal, D L}
}
@article {Hu_2016_turbmodelcases_AIAAJ,
	title = {Application of Higher-order Adaptive Method to Reynolds-Averaged Navier{\textendash}Stokes Test Cases},
	journal = {AIAA Journal},
	volume = {54},
	number = {9},
	year = {2016},
	doi = {10.2514/1.J054558},
	author = {Hu, Y and Wagner, C F and Allmaras, S R and Galbraith, M C and Darmofal, D L}
}
@conference {Darmofal_2013_PXOverview,
	title = {An adaptive, higher-order discontinuous Galerkin finite element method for aerodynamics},
	booktitle = {AIAA conference paper},
	number = {2013-2871},
	year = {2013},
	author = {Darmofal, D L and Allmaras, S R and Yano, M and Kudo, J}
}
