%0 Journal Article %J SIAM Journal on Scientific Computing %D 2021 %T Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods %A Ornela Mulita %A Stefano Giani %A Luca Heltai %B SIAM Journal on Scientific Computing %G eng %0 Journal Article %J Computational Methods in Applied Mathematics %D 2021 %T Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems %A Stefano Giani %A Luka Grubisic %A Luca Heltai %A Ornela Mulita %B Computational Methods in Applied Mathematics %V 21 %P 385-405 %G eng %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 %0 Book Section %B Building bridges: connections and challenges in modern approaches to numerical partial differential equations %D 2016 %T Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains %A Antonietti, Paola F. %A Andrea Cangiani %A Collis, Joe %A Dong, Zhaonan %A E.H. Georgoulis %A Stefano Giani %A Houston, Paul %B Building bridges: connections and challenges in modern approaches to numerical partial differential equations %S Lect. Notes Comput. Sci. Eng. %I Springer, [Cham] %V 114 %P 279–308 %G eng