| DC Field | Value | Language |
|---|---|---|
| dc.contributor | Department of Applied Mathematics | en_US |
| dc.creator | Akrivis, G | en_US |
| dc.creator | Li, B | en_US |
| dc.date.accessioned | 2021-04-28T01:17:21Z | - |
| dc.date.available | 2021-04-28T01:17:21Z | - |
| dc.identifier.issn | 0272-4979 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10397/89651 | - |
| dc.language.iso | en | en_US |
| dc.publisher | Oxford University Press | en_US |
| dc.title | Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation | en_US |
| dc.type | Journal/Magazine Article | en_US |
| dc.identifier.doi | 10.1093/imanum/draa065 | en_US |
| dcterms.abstract | For a class of compatible profiles of initial data describing bulk phase regions separated by transition zones, we approximate the Cauchy problem of the Allen–Cahn (AC) phase field equation by an initial-boundary value problem in a bounded domain with the Dirichlet boundary condition. The initial-boundary value problem is discretized in time by the backward difference formulae (BDF) of order 1⩽q⩽5 and in space by the Galerkin finite element method of polynomial degree r−1, with r⩾2. We establish an error estimate of O(τqε−q−12+hrε−r−12+e−c/ε) with explicit dependence on the small parameter ε describing the thickness of the phase transition layer. The analysis utilizes the maximum-norm stability of BDF and finite element methods with respect to the boundary data, the discrete maximal Lp-regularity of BDF methods for parabolic equations and the Nevanlinna–Odeh multiplier technique combined with a time-dependent inner product motivated by a spectrum estimate of the linearized AC operator. | en_US |
| dcterms.accessRights | embargoed access | en_US |
| dcterms.bibliographicCitation | IMA journal of numerical analysis, draa065, https://doi.org/10.1093/imanum/draa065 | en_US |
| dcterms.isPartOf | IMA journal of numerical analysis | en_US |
| dcterms.issued | 2020 | - |
| dc.identifier.eissn | 1464-3642 | en_US |
| dc.description.validate | 202104 bcwh | en_US |
| dc.description.oa | Not applicable | en_US |
| dc.identifier.FolderNumber | a0602-n11 | - |
| dc.identifier.SubFormID | 556 | - |
| dc.description.fundingSource | RGC | en_US |
| dc.description.fundingText | 15300519 | en_US |
| dc.description.pubStatus | Early release | en_US |
| dc.date.embargo | 0000-00-00 (to be updated) | en_US |
| Appears in Collections: | Journal/Magazine Article | |
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