ETNA - Electronic Transactions on Numerical Analysis, pp. 99-122, 2024/02/29
A posteriori error estimates in the maximum norm are studied forvarious time-semidiscretisations applied to a class of linear parabolic equations. We summarise results from the literature and present some new improved error bounds. Crucial ingredients are certain bounds in the $L_1$-norm for the Green's function associated with the parabolic operator and its derivatives.
Keywords: parabolic problems, maximum-norm a posteriori error estimates, backward Euler, Crank–Nicolson, extrapolation, discontinuous Galerkin–Radau, backward differentiation formulae, Green's function