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Main Title: Discrete versions of Gronwall's lemma and their application to the numerical analysis of parabolic problems
Author(s): Emmrich, Etienne
Type: Research Paper
Abstract: The well-known Gronwall lemma often serves as a major tool for the analysis of time-dependent problems via energy methods. However, there is the need for a similar tool when considering temporal discretizations of evolutionary problems. With the paper in hand, the author wishes to give an overview of some discrete versions of the Gronwall lemma and presents a unified approach. In particular, new discrete versions of the lemma in its differential form and their application, showing decay behaviour for discretized parabolic problems, are studied. These versions give effective tools for the stability and error analysis of the temporal semi-discretization of parabolic problems covering non-homogeneous problems as well as approximations with variable step sizes.
Subject(s): Gronwall-type inequality
differential inequality
difference inequality
parabolic differential equation
temporal discretization
Euler method
Issue Date: 1-Jul-1999
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
39A12 Discrete version of topics in analysis
65M12 Stability and convergence of numerical methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1999, 637
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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