@article {CANGIANI20193090,
	title = {hp-adaptive discontinuous Galerkin methods for non-stationary convection{\textendash}diffusion problems},
	journal = {Computers \& Mathematics with Applications},
	volume = {78},
	number = {9},
	year = {2019},
	note = {Applications of Partial Differential Equations in Science and Engineering},
	pages = {3090-3104},
	abstract = {An a posteriori error estimator for the error in the (L2(H1)+L$\infty$(L2))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection{\textendash}diffusion initial/boundary value problems is derived, allowing for anisotropic elements. The proposed error estimator is used to drive an hp-space{\textendash}time adaptive algorithm wherein directional mesh refinement is employed to give rise to highly anisotropic elements able to accurately capture layers. The performance of the hp-space{\textendash}time adaptive algorithm is assessed via a number of standard test problems characterised by sharp and/or moving layers.},
	keywords = {A posteriori error estimation, Adaptive finite element methods, Anisotropic meshes, Discontinuous Galerkin, Unsteady convection{\textendash}diffusion},
	issn = {0898-1221},
	doi = {https://doi.org/10.1016/j.camwa.2019.04.002},
	url = {https://www.sciencedirect.com/science/article/pii/S0898122119302007},
	author = {Andrea Cangiani and E.H. Georgoulis and Stefano Giani and S. Metcalfe}
}
@book {MR3729265,
	title = {$hp$-version discontinuous Galerkin methods on polygonal and polyhedral meshes},
	series = {SpringerBriefs in Mathematics},
	year = {2017},
	pages = {viii+131},
	publisher = {Springer, Cham},
	organization = {Springer, Cham},
	isbn = {978-3-319-67671-5; 978-3-319-67673-9},
	author = {Andrea Cangiani and Dong, Zhaonan and E.H. Georgoulis and Houston, Paul}
}
@article {MR3672375,
	title = {$hp$-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes},
	journal = {SIAM J. Sci. Comput.},
	volume = {39},
	number = {4},
	year = {2017},
	pages = {A1251{\textendash}A1279},
	issn = {1064-8275},
	doi = {10.1137/16M1073285},
	url = {https://doi.org/10.1137/16M1073285},
	author = {Andrea Cangiani and Dong, Zhaonan and E.H. Georgoulis}
}
@article {MR3507270,
	title = {$hp$-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes},
	journal = {ESAIM Math. Model. Numer. Anal.},
	volume = {50},
	number = {3},
	year = {2016},
	pages = {699{\textendash}725},
	issn = {0764-583X},
	doi = {10.1051/m2an/2015059},
	url = {https://doi.org/10.1051/m2an/2015059},
	author = {Andrea Cangiani and Dong, Zhaonan and E.H. Georgoulis and Houston, Paul}
}
@article {MR3211116,
	title = {$hp$-version discontinuous Galerkin methods on polygonal and polyhedral meshes},
	journal = {Math. Models Methods Appl. Sci.},
	volume = {24},
	number = {10},
	year = {2014},
	pages = {2009{\textendash}2041},
	issn = {0218-2025},
	doi = {10.1142/S0218202514500146},
	url = {https://doi.org/10.1142/S0218202514500146},
	author = {Andrea Cangiani and E.H. Georgoulis and Houston, Paul}
}
