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 …

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 …

A popular approach for proving a posteriori error bounds in various norms for evolution
problems with partial differential equations uses reconstruction operators to recover …

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 ↪ …

In this article, we develop an adaptive procedure for the numerical solution of semilinear
parabolic problems with possible singular perturbations. Our approach combines a …

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 …

We construct, analyze and numerically validate a posteriori error estimates for conservative
discontinuous Galerkin (DG) schemes for the Generalized Korteweg-de Vries (GKdV) …

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 …

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 …

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 …