@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 = {

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.

}, 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 {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 ' \> 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} }