Volume 60, pp. 99-122, 2024.

A review of maximum-norm a posteriori error bounds for time-semidiscretisations of parabolic equations

Torsten Linss, Natalia Kopteva, Goran Radojev, and Martin Ossadnik


A posteriori error estimates in the maximum norm are studied for various 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.

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Key words

parabolic problems, maximum-norm a posteriori error estimates, backward Euler, Crank–Nicolson, extrapolation, discontinuous Galerkin–Radau, backward differentiation formulae, Green's function

AMS subject classifications

65M15, 65M60

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