Adaptivity and blow-up detection for nonlinear evolution problems
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 …
based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem …
hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems
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 existence …
approximations to nonlinear initial value problems with an emphasis on finite-time existence …
Lower bounds, elliptic reconstruction and a posteriori error control of parabolic problems
EH Georgoulis, CG Makridakis - IMA Journal of Numerical …, 2023 - academic.oup.com
A popular approach for proving a posteriori error bounds in various norms for evolution
problems with partial differential equations uses reconstruction operators to recover …
problems with partial differential equations uses reconstruction operators to recover …
A Posteriori Error Analysis for Implicit–Explicit hp-Discontinuous Galerkin Timestepping Methods for Semilinear Parabolic Problems
A posteriori error estimates in the L_ ∞ (H) L∞(H)-and L_2 (V) L 2 (V)-norms are derived for
fully-discrete space–time methods discretising semilinear parabolic problems; here V ↪ H ↪ …
fully-discrete space–time methods discretising semilinear parabolic problems; here V ↪ H ↪ …
An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations
M Amrein, TP Wihler - IMA Journal of Numerical Analysis, 2017 - academic.oup.com
In this article, we develop an adaptive procedure for the numerical solution of semilinear
parabolic problems with possible singular perturbations. Our approach combines a …
parabolic problems with possible singular perturbations. Our approach combines a …
[PDF][PDF] Discontinuous Galerkin timestepping for nonlinear parabolic problems
MAM Sabawi - 2018 - figshare.le.ac.uk
We study space–time finite element methods for semilinear parabolic problems in (1+ d)–
dimensions for d= 2, 3. The discretisation in time is based on the discontinuous Galerkin …
dimensions for d= 2, 3. The discretisation in time is based on the discontinuous Galerkin …
A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation
O Karakashian, C Makridakis - Mathematics of Computation, 2015 - ams.org
We construct, analyze and numerically validate a posteriori error estimates for conservative
discontinuous Galerkin (DG) schemes for the Generalized Korteweg-de Vries (GKdV) …
discontinuous Galerkin (DG) schemes for the Generalized Korteweg-de Vries (GKdV) …
A Posteriori Error Analysis for Evolution Nonlinear Schrodinger Equations Up to the Critical Exponent
T Katsaounis, I Kyza - SIAM Journal on Numerical Analysis, 2018 - SIAM
We provide a posteriori error estimates in the L^∞(0,T;L^2(Ω))-norm for relaxation time
discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger …
discrete and fully discrete schemes for a class of evolution nonlinear Schrödinger …
Adaptive discontinuous Galerkin methods for nonlinear parabolic problems
SA Metcalfe - arXiv preprint arXiv:1504.02646, 2015 - arxiv.org
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) discretisations. We …
problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We …
Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method
We consider a blow-up solution for a strongly perturbed semilinear heat equation with
Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we …
Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we …