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Article: The BDF3/EP3 Scheme for MBE with No Slope Selection is Stable

TitleThe BDF3/EP3 Scheme for MBE with No Slope Selection is Stable
Authors
KeywordsEnergy stable
MBE
No slope selection
Phase field
Stability
Issue Date2021
Citation
Journal of Scientific Computing, 2021, v. 89, n. 2, article no. 33 How to Cite?
AbstractWe consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in time with implicit treatment of the surface diffusion term. The nonlinear term is approximated by a third order explicit extrapolation (EP3) formula. We exhibit mild time step constraints under which the modified energy dissipation law holds. We break the second Dahlquist barrier and develop a new theoretical framework to prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional result for third order BDF methods applied to the MBE models without introducing any stabilization term or fictitious variable. The analysis can be generalized to a restrictive class of phase field models whose nonlinearity has bounded derivatives. A novel theoretical framework is also established for the error analysis of high order methods.
Persistent Identifierhttp://hdl.handle.net/10722/327357
ISSN
2023 Impact Factor: 2.8
2023 SCImago Journal Rankings: 1.248
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLi, Dong-
dc.contributor.authorQuan, Chaoyu-
dc.contributor.authorYang, Wen-
dc.date.accessioned2023-03-31T05:30:45Z-
dc.date.available2023-03-31T05:30:45Z-
dc.date.issued2021-
dc.identifier.citationJournal of Scientific Computing, 2021, v. 89, n. 2, article no. 33-
dc.identifier.issn0885-7474-
dc.identifier.urihttp://hdl.handle.net/10722/327357-
dc.description.abstractWe consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. We employ a third order backward differentiation (BDF3) in time with implicit treatment of the surface diffusion term. The nonlinear term is approximated by a third order explicit extrapolation (EP3) formula. We exhibit mild time step constraints under which the modified energy dissipation law holds. We break the second Dahlquist barrier and develop a new theoretical framework to prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional result for third order BDF methods applied to the MBE models without introducing any stabilization term or fictitious variable. The analysis can be generalized to a restrictive class of phase field models whose nonlinearity has bounded derivatives. A novel theoretical framework is also established for the error analysis of high order methods.-
dc.languageeng-
dc.relation.ispartofJournal of Scientific Computing-
dc.subjectEnergy stable-
dc.subjectMBE-
dc.subjectNo slope selection-
dc.subjectPhase field-
dc.subjectStability-
dc.titleThe BDF3/EP3 Scheme for MBE with No Slope Selection is Stable-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10915-021-01642-5-
dc.identifier.scopuseid_2-s2.0-85115620719-
dc.identifier.volume89-
dc.identifier.issue2-
dc.identifier.spagearticle no. 33-
dc.identifier.epagearticle no. 33-
dc.identifier.eissn1573-7691-
dc.identifier.isiWOS:000698661900001-

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