TY - JOUR T1 - hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems JF - Computers & Mathematics with Applications Y1 - 2019 A1 - Andrea Cangiani A1 - E.H. Georgoulis A1 - Stefano Giani A1 - S. Metcalfe KW - A posteriori error estimation KW - Adaptive finite element methods KW - Anisotropic meshes KW - Discontinuous Galerkin KW - Unsteady convection–diffusion AB - 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. VL - 78 UR - https://www.sciencedirect.com/science/article/pii/S0898122119302007 N1 - Applications of Partial Differential Equations in Science and Engineering ER -