11 citations · 25 across the 8 of their papers we have counts for
8 papers
Conditional a posteriori error bounds for high order DG time stepping approximations of semilinear heat models with blow-up
Stephen Metcalfe, Thomas P. Wihler
This work is concerned with the development of an adaptive numerical method for semilinear heat flow models featuring a general (possibly) nonlinear reaction term that may cause th…
A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza +1
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Cr…
A robust quasi-optimal test norm for a DPG discretization of the convection-diffusion equation
Stephen Metcalfe, Siva Nadarajah
In this work, we propose a new quasi-optimal test norm for a discontinuous Petrov-Galerkin (DPG) discretization of the ultra-weak formulation of the convection-diffusion equation.…
Pointwise a posteriori error bounds for blow-up in the semilinear heat equation
Irene Kyza, Stephen Metcalfe
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for the semilinear heat equation with a general…
-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems
Irene Kyza, Stephen Metcalfe, Thomas Wihler
This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existe…
Adaptive discontinuous Galerkin methods for nonlinear parabolic problems
Stephen Arthur Metcalfe
This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisatio…
Adaptivity and blow-up detection for nonlinear evolution problems
Andrea Cangiani, Emmanuil H. Georgoulis, Irene Kyza +1
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem w…
An a posteriori error estimator for discontinuous Galerkin methods for non-stationary convection-diffusion problems
Andrea Cangiani, Emmanuil H. Georgoulis, Stephen Metcalfe
This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion…