A review of maximum-norm a posteriori error bounds for time-semidiscretisations of parabolic equations
Torsten Lin\ss, Natalia Kopteva, Goran Radojev, Martin Ossadnik
TL;DR
This paper reviews and improves maximum-norm a posteriori error bounds for time-semidiscretisations of linear parabolic equations, emphasizing Green's function bounds in $L_1$ norm.
Contribution
It summarizes existing results and introduces new, sharper error bounds for parabolic equations using Green's function estimates.
Findings
Improved maximum-norm error bounds for time-semidiscretisations.
Identification of key Green's function bounds in $L_1$ norm.
Enhanced understanding of a posteriori error estimation techniques.
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 norm for the Green's function associated with the parabolic operator and its derivatives.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics