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Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

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Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

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dc.contributor.author Moreno-Navarro, Pablo es_ES
dc.contributor.author Ibrahimbegovic, Adnan es_ES
dc.contributor.author Ospina, Alejandro es_ES
dc.date.accessioned 2021-05-12T03:31:47Z
dc.date.available 2021-05-12T03:31:47Z
dc.date.issued 2020-01 es_ES
dc.identifier.issn 0178-7675 es_ES
dc.identifier.uri http://hdl.handle.net/10251/166203
dc.description The final publication is available at link.springer.com es_ES
dc.description.abstract [EN] In this paper we propose different multi-field variational formulations for electrostatics and magnetostatics, which can provide optimal discrete approximation of any particular vector field. The proposed formulations are constructed by appealing to mechanics point of view amenable to using general constitutive equations, which is quite different from electrostatics and magnetostatics formulations typical of physics and electrical engineering focusing on the corresponding global form suitable only for linear case. In particular, the formulations we propose can be combined with mixed discrete approximations that can ensure the continuity of tangential component of electric ormagnetic field and normal component of electric displacement and magnetic flux even for low order interpolations. The choice of this kind is quite different from currently favorite choice of high order finite element interpolations used for coupling electromagnetism with mechanics. The discrete approximation is based upon Whitney's interpolations representing the vector fields in terms of corresponding differential forms, with electric and magnetic fields as one-form and electric displacement and magnetic flux as two-form. The implementation of interpolations of this kind is made for 3D tetrahedron elements with non-standard approximation parameters defined not only at vertices (for zero-form), but at edges (for one-form) and at facets (for two-form). The results of several numerical simulations are presented to illustrate the performance of different formulations proposed herein. es_ES
dc.description.sponsorship This work was supported jointly by Haut-deFrance Region (CR Picardie) (120-2015-RDISTRUCT-000010 and RDISTRUCT-000010) and EU funding (FEDER) for Chaire-deMecanique (120-2015-RDISTRUCTF-000010 and RDISTRUCTI000004). AI was also supported by IUF. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Computational Mechanics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Electrostatics es_ES
dc.subject Magnetostatics es_ES
dc.subject Variational method es_ES
dc.subject Whitney's element es_ES
dc.subject Homogenization es_ES
dc.subject Elasticity es_ES
dc.subject Framework es_ES
dc.subject.classification INGENIERIA AEROESPACIAL es_ES
dc.title Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00466-019-01751-x es_ES
dc.relation.projectID info:eu-repo/grantAgreement/EC//RDISTRUCTI-000004/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/EC//120-2015-RDISTRUCTF-000010/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Mecánica de los Medios Continuos y Teoría de Estructuras - Departament de Mecànica dels Medis Continus i Teoria d'Estructures es_ES
dc.description.bibliographicCitation Moreno-Navarro, P.; Ibrahimbegovic, A.; Ospina, A. (2020). Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics. Computational Mechanics. 65(1):41-59. https://doi.org/10.1007/s00466-019-01751-x es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00466-019-01751-x es_ES
dc.description.upvformatpinicio 41 es_ES
dc.description.upvformatpfin 59 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 65 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\411687 es_ES
dc.contributor.funder European Commission es_ES
dc.contributor.funder Conseil Régional Hauts-de-France es_ES
dc.contributor.funder Institut Universitaire de France es_ES
dc.contributor.funder European Regional Development Fund es_ES
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