| Title | hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Cangiani, A, Georgoulis, EH, Giani, S, Metcalfe, S |
| Journal | Computers & Mathematics with Applications |
| Volume | 78 |
| Pagination | 3090-3104 |
| ISSN | 0898-1221 |
| Keywords | A posteriori error estimation; Adaptive finite element methods; Anisotropic meshes; Discontinuous Galerkin; Unsteady convection–diffusion |
| Abstract | 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. |
| URL | https://www.sciencedirect.com/science/article/pii/S0898122119302007 |
| DOI | 10.1016/j.camwa.2019.04.002 |