dc.creator | Gutiérrez Santacreu, Juan Vicente | es |
dc.creator | Restelli, Marco | es |
dc.date.accessioned | 2019-10-18T09:22:45Z | |
dc.date.available | 2019-10-18T09:22:45Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Gutiérrez Santacreu, J.V. y Restelli, M. (2017). Inf-Sup Stable Finite Element Methods for the Landau--Lifshitz--Gilbert and Harmonic Map Heat Flow Equations. SIAM Journal on Numerical Analysis, 55 (6), 2565-2591. | |
dc.identifier.issn | 0036-1429 | es |
dc.identifier.uri | https://hdl.handle.net/11441/89745 | |
dc.description.abstract | In this paper we propose and analyze a finite element method for both the harmonic map
heat and Landau–Lifshitz–Gilbert equation, the time variable remaining continuous. Our starting
point is to set out a unified saddle point approach for both problems in order to impose the unit
sphere constraint at the nodes since the only polynomial function satisfying the unit sphere constraint
everywhere are constants. A proper inf-sup condition is proved for the Lagrange multiplier leading to
the well-posedness of the unified formulation. A priori energy estimates are shown for the proposed
method.
When time integrations are combined with the saddle point finite element approximation some
extra elaborations are required in order to ensure both a priori energy estimates for the director or
magnetization vector depending on the model and an inf-sup condition for the Lagrange multiplier.
This is due to the fact that the unit length at the nodes is not satisfied in general when a time
integration is performed. We will carry out a linear Euler time-stepping method and a non-linear
Crank–Nicolson method. The latter is solved by using the former as a non-linear solver. | es |
dc.description.sponsorship | Ministerio de Economía y Competitividad MTM2015-69875-P | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | SIAM: Society for Industrial and Applied Mathematics | es |
dc.relation.ispartof | SIAM Journal on Numerical Analysis, 55 (6), 2565-2591. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Finite-element approximation | es |
dc.subject | Inf-sup conditions | es |
dc.subject | Landau–Lifshitz–Gilbert equation | es |
dc.subject | Harmonic map heat flow equation | es |
dc.title | Inf-Sup Stable Finite Element Methods for the Landau--Lifshitz--Gilbert and Harmonic Map Heat Flow Equations | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) | es |
dc.relation.projectID | MTM2015-69875-P | es |
dc.relation.publisherversion | https://epubs.siam.org/doi/abs/10.1137/17M1116799 | es |
dc.identifier.doi | 10.1137/17M1116799 | es |
idus.format.extent | 21 | es |
dc.journaltitle | SIAM Journal on Numerical Analysis | es |
dc.publication.volumen | 55 | es |
dc.publication.issue | 6 | es |
dc.publication.initialPage | 2565 | es |
dc.publication.endPage | 2591 | es |