A REVIEW OF MAXIMUM-NORM A POSTERIORI ERROR BOUNDS FOR TIME-SEMIDISCRETISATIONS OF PARABOLIC EQUATIONS

Torsten Linss; Natalia Kopteva; Goran Radojev; Martin Ossadnik

doi:10.1553/etna_vol60s99

A REVIEW OF MAXIMUM-NORM A POSTERIORI ERROR BOUNDS FOR TIME-SEMIDISCRETISATIONS OF PARABOLIC EQUATIONS

Torsten Linss, Natalia Kopteva, Goran Radojev, Martin Ossadnik

Research output: Contribution to journal › Review article › peer-review

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 L1-norm for the Green’s function associated with the parabolic operator and its derivatives.

Original language	English
Pages (from-to)	99-122
Number of pages	24
Journal	Electronic Transactions on Numerical Analysis
Volume	60
DOIs	https://doi.org/10.1553/etna_vol60s99
Publication status	Published - 2024

Keywords

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

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10.1553/etna_vol60s99

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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 L1-norm for the Green{\textquoteright}s function associated with the parabolic operator and its derivatives.",

keywords = "Crank–Nicolson, Green{\textquoteright}s function, backward Euler, backward differentiation formulae, discontinuous Galerkin–Radau, extrapolation, maximum-norm a posteriori error estimates, parabolic problems",

author = "Torsten Linss and Natalia Kopteva and Goran Radojev and Martin Ossadnik",

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AU - Radojev, Goran

AU - Ossadnik, Martin

PY - 2024

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AB - 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 L1-norm for the Green’s function associated with the parabolic operator and its derivatives.

KW - Crank–Nicolson

KW - Green’s function

KW - backward Euler

KW - backward differentiation formulae

KW - discontinuous Galerkin–Radau

KW - extrapolation

KW - maximum-norm a posteriori error estimates

KW - parabolic problems

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JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

ER -

A REVIEW OF MAXIMUM-NORM A POSTERIORI ERROR BOUNDS FOR TIME-SEMIDISCRETISATIONS OF PARABOLIC EQUATIONS

Abstract

Keywords

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