%0 Journal Article %J Computers & Mathematics with Applications %D 2019 %T hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems %A Andrea Cangiani %A E.H. Georgoulis %A Stefano Giani %A S. Metcalfe %K A posteriori error estimation %K Adaptive finite element methods %K Anisotropic meshes %K Discontinuous Galerkin %K Unsteady convection–diffusion %X An a posteriori error estimator for the error in the (L2(H1)+L∞(L2))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection–diffusion initial/boundary value problems is derived, allowing for anisotropic elements. The proposed error estimator is used to drive an hp-space–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–time adaptive algorithm is assessed via a number of standard test problems characterised by sharp and/or moving layers. %B Computers & Mathematics with Applications %V 78 %P 3090-3104 %G eng %U https://www.sciencedirect.com/science/article/pii/S0898122119302007 %R https://doi.org/10.1016/j.camwa.2019.04.002