Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/90514
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorDu, Qen_US
dc.creatorJu, Len_US
dc.creatorLi, Xen_US
dc.creatorQiao, Zen_US
dc.date.accessioned2021-07-15T02:12:05Z-
dc.date.available2021-07-15T02:12:05Z-
dc.identifier.issn0036-1445en_US
dc.identifier.urihttp://hdl.handle.net/10397/90514-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rightsFirst Published in SIAM Review in Volume 63, Issue 2, published by the Society for Industrial and Applied Mathematics (SIAM)en_US
dc.rights© 2021, Society for Industrial and Applied Mathematicsen_US
dc.rightsUnauthorized reproduction of this article is prohibited.en_US
dc.subjectEnergy stabilityen_US
dc.subjectError estimateen_US
dc.subjectExponential time differencingen_US
dc.subjectMaximum bound principleen_US
dc.subjectNumerical approximationen_US
dc.subjectSemilinear parabolic equationen_US
dc.titleMaximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemesen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage317en_US
dc.identifier.epage359en_US
dc.identifier.volume63en_US
dc.identifier.issue2en_US
dc.identifier.doi10.1137/19M1243750en_US
dcterms.abstractThe ubiquity of semilinear parabolic equations is clear from their numerous applications ranging from physics and biology to materials and social sciences. In this paper, we consider a practically desirable property for a class of semilinear parabolic equations of the abstract form ut = L u + f[u], with L a linear dissipative operator and f a nonlinear operator in space, namely, a time-invariant maximum bound principle, in the sense that the timedependent solution u preserves for all time a uniform pointwise bound in absolute value imposed by its initial and boundary conditions. We first study an analytical framework for sufficient conditions on L and f that lead to such a maximum bound principle for the time-continuous dynamic system of infinite or finite dimensions. Then we utilize a suitable exponential time-differencing approach with a properly chosen generator of the contraction semigroup to develop first- and second-order accurate temporal discretization schemes that satisfy the maximum bound principle unconditionally in the time-discrete setting. Error estimates of the proposed schemes are derived along with their energy stability. Extensions to vector- and matrix-valued systems are also discussed. We demonstrate that the abstract framework and analysis techniques developed here offer an effective and unified approach to studying the maximum bound principle of the abstract evolution equation that covers a wide variety of well-known models and their numerical discretization schemes. Some numerical experiments are also carried out to verify the theoretical results.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM review, 2021, v. 63, no. 2, p. 317-359en_US
dcterms.isPartOfSIAM reviewen_US
dcterms.issued2021-
dc.identifier.scopus2-s2.0-85102112070-
dc.identifier.eissn1095-7200en_US
dc.description.validate202107 bcvcen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera0966-n02-
dc.identifier.SubFormID2247-
dc.description.fundingSourceRGCen_US
dc.description.fundingSourceOthersen_US
dc.description.fundingTextRGC: 15302214, 15325816en_US
dc.description.fundingTextOthers: 1-ZE33en_US
dc.description.pubStatusPublisheden_US
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