Discrete versions of Gronwall's lemma and their application to the numerical analysis of parabolic problems

dc.contributor.authorEmmrich, Etienne
dc.date.accessioned2021-12-17T10:16:55Z
dc.date.available2021-12-17T10:16:55Z
dc.date.issued1999-07-01
dc.description.abstractThe 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.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15941
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14714
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherGronwall-type inequalityen
dc.subject.otherdifferential inequalityen
dc.subject.otherdifference inequalityen
dc.subject.otherparabolic differential equationen
dc.subject.othertemporal discretizationen
dc.subject.otherEuler methoden
dc.titleDiscrete versions of Gronwall's lemma and their application to the numerical analysis of parabolic problemsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber1999, 637en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200026D10 Inequalities involving derivatives and differential and integral operatorsen
tub.subject.msc200026D15 Inequalities for sums, series and integralsen
tub.subject.msc200039A12 Discrete version of topics in analysisen
tub.subject.msc200065M12 Stability and convergence of numerical methodsen

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