Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/89358
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Li, B | en_US |
dc.creator | Yang, J | en_US |
dc.creator | Zhou, Z | en_US |
dc.date.accessioned | 2021-03-18T03:04:40Z | - |
dc.date.available | 2021-03-18T03:04:40Z | - |
dc.identifier.issn | 1064-8275 | en_US |
dc.identifier.uri | http://hdl.handle.net/10397/89358 | - |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.rights | © 2020, Society for Industrial and Applied Mathematics. | en_US |
dc.rights | Unauthorized reproduction of this article is prohibited. | en_US |
dc.rights | First 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.subject | Allen-Cahn equation | en_US |
dc.subject | Cut-off | en_US |
dc.subject | Exponential integrator | en_US |
dc.subject | High order | en_US |
dc.subject | Lumped mass | en_US |
dc.subject | Maximum principle | en_US |
dc.subject | Parabolic equation | en_US |
dc.title | Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | A3957 | en_US |
dc.identifier.epage | A3968 | en_US |
dc.identifier.volume | 42 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.doi | 10.1137/20M1333456 | en_US |
dcterms.abstract | A 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.accessRights | open access | en_US |
dcterms.bibliographicCitation | SIAM journal on scientific computing, 2020, v. 42, no. 6, p. A3957-A3968 | en_US |
dcterms.isPartOf | SIAM journal on scientific computing | en_US |
dcterms.issued | 2020 | - |
dc.identifier.scopus | 2-s2.0-85099052166 | - |
dc.identifier.eissn | 1095-7197 | en_US |
dc.description.validate | 202103 bcvc | en_US |
dc.description.oa | Accepted Manuscript | en_US |
dc.identifier.FolderNumber | a0602-n06 | - |
dc.identifier.SubFormID | 551 | - |
dc.description.fundingSource | RGC | en_US |
dc.description.fundingText | 15300519 | en_US |
dc.description.pubStatus | Published | en_US |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
a0602-n06_cut_off_rev.pdf | Pre-Published version | 783.95 kB | Adobe PDF | View/Open |
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