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A review of maximum-norm a posteriori error bounds for time-semidiscretisations of parabolic equations (2212.11540v1)
Published 22 Dec 2022 in math.NA and cs.NA
Abstract: 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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