Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/89358
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorLi, Ben_US
dc.creatorYang, Jen_US
dc.creatorZhou, Zen_US
dc.date.accessioned2021-03-18T03:04:40Z-
dc.date.available2021-03-18T03:04:40Z-
dc.identifier.issn1064-8275en_US
dc.identifier.urihttp://hdl.handle.net/10397/89358-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2020, Society for Industrial and Applied Mathematics.en_US
dc.rightsUnauthorized reproduction of this article is prohibited.en_US
dc.rightsFirst Published in SIAM Journal on SIAM Journal on Scientific Computing in Volume 42, Issue 6, published by the Society for Industrial and Applied Mathematics (SIAM)en_US
dc.subjectAllen-Cahn equationen_US
dc.subjectCut-offen_US
dc.subjectExponential integratoren_US
dc.subjectHigh orderen_US
dc.subjectLumped massen_US
dc.subjectMaximum principleen_US
dc.subjectParabolic equationen_US
dc.titleArbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equationsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spageA3957en_US
dc.identifier.epageA3968en_US
dc.identifier.volume42en_US
dc.identifier.issue6en_US
dc.identifier.doi10.1137/20M1333456en_US
dcterms.abstractA new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen-Cahn equation. The proposed method consists of a kth-order multistep exponential integrator in time and a lumped mass finite element method in space with piecewise rth-order polynomials and Gauss-Lobatto quadrature. At every time level, the extra values violating the maximum principle are eliminated at the finite element nodal points by a cut-off operation. The remaining values at the nodal points satisfy the maximum principle and are proved to be convergent with an error bound of O(τ k + hr). The accuracy can be made arbitrarily high-order by choosing large k and r. Extensive numerical results are provided to illustrate the accuracy of the proposed method and the effectiveness in capturing the pattern of phase-field problems.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on scientific computing, 2020, v. 42, no. 6, p. A3957-A3968en_US
dcterms.isPartOfSIAM journal on scientific computingen_US
dcterms.issued2020-
dc.identifier.scopus2-s2.0-85099052166-
dc.identifier.eissn1095-7197en_US
dc.description.validate202103 bcvcen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumbera0602-n06-
dc.identifier.SubFormID551-
dc.description.fundingSourceRGCen_US
dc.description.fundingText15300519en_US
dc.description.pubStatusPublisheden_US
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