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Método de elementos finitos para un problema de corrientes inducidas axisimetrico

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dc.contributor.advisorReales, Carlosspa
dc.contributor.authorOtero Pantoja, Jean Carlos
dc.date.accessioned2022-03-28T02:11:20Z
dc.date.available2022-03-28T02:11:20Z
dc.date.issued2022-03-25
dc.description.abstractIn this work a Finite Element Method for an Axisymmetric Eddy Current problem will be studied. A variational formulation of the problem will be established and the existence and uniqueness of the solution will be proved, making use of some results of the Functional Analysis. Next, a discretization of the variational problem will be established and error estimates will be tested.spa
dc.description.degreelevelPregradospa
dc.description.degreenameMatemático(a)spa
dc.description.modalityMonografíasspa
dc.description.resumenEn este trabajo se estudiará un Método de Elementos Finitos para un problema de Corrientes Inducidas Axisimétrico. Se establecerá una formulación variacional del problema y se probará la existencia y unicidad de la solución, haciendo uso de algunos resultados del Análisis Funcional. Seguidamente, se establecerá una discretización del problema variacional y se probarán estimativos de error.
dc.description.tableofcontentsResumen ivspa
dc.description.tableofcontentsAbstract vspa
dc.description.tableofcontents1. Preliminares 5spa
dc.description.tableofcontents1.1. Espacios de Hilbert . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5spa
dc.description.tableofcontents1.2. Espacios de Sobolev ponderados . . . . . . . . . . . . . . . . . . . . . 14spa
dc.description.tableofcontents2. Problema de corrientes inducidas 18spa
dc.description.tableofcontents2.1. Coordenadas Cilíndricas y Espacios de Sobolev . . . . . . . . . . . . 18spa
dc.description.tableofcontents2.2. Planteamiento del Problema . . . . . . . . . . . . . . . . . . . . . . . 20spa
dc.description.tableofcontents2.3. Formulación variacional . . . . . . . . . . . . . . . . . . . . . . . . . 25spa
dc.description.tableofcontents3. Discretización por Elementos Finitos 34spa
dc.description.tableofcontents3.1. Problema Discreto . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34spa
dc.description.tableofcontents3.2. Análisis del error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37spa
dc.description.tableofcontents3.3. Estimaciones de Error de las variables físicas. . . . . . . . . . . . . . 39spa
dc.description.tableofcontentsBibliografía . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.urihttps://repositorio.unicordoba.edu.co/handle/ucordoba/5056
dc.language.isospaspa
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.publisher.placeMontería, Córdoba, Colombiaspa
dc.publisher.programMatemáticaspa
dc.rightsCopyright Universidad de Córdoba, 2022spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.creativecommonsAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)spa
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/spa
dc.subject.keywordsVariational formulationspa
dc.subject.proposalFormulación variacionalspa
dc.titleMétodo de elementos finitos para un problema de corrientes inducidas axisimetricospa
dc.typeTrabajo de grado - Pregradospa
dc.type.coarhttp://purl.org/coar/resource_type/c_7a1fspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/bachelorThesisspa
dc.type.versioninfo:eu-repo/semantics/submittedVersionspa
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dcterms.references[10] Assous, F., Ciarlet Jr, P., Labrunie, S. & Segré, J. (2003) Numeri cal solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method, J. Comput. Phys. 191, 147–176.spa
dcterms.references[11] Belhachmi, Z., Bernardi, C. & Deparis, S. (2002) Weighted Clément ope rator and application to the finite element discretization of the axisymmetric Sto kesspa
dcterms.references[12] Bermúdez, A., Gómez, D., Muñiz, M.C. & Salgado, P. (2007a) Transient numerical simulation of a thermoelectrical problem in cylindrical induction hea ting furnaces, Advspa
dcterms.references[13] Bermúdez, A., Gómez, D., Muñiz, M.C. & Salgado, P. (2007b) A FEM/BEM for axisymmetric electromagnetic and thermal modelling of induc tiospa
dcterms.references[14] Bermúdez, A., Gómez, D., Muñiz, M.C., Salgado, P. & Vázquez, R. (2008) Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace (submitted).spa
dcterms.references[15] Bermúdez, A., Reales, C., Rodríguez, R.& Salgado, P.(2010) Numeri cal analysis of a finite-element method for the axisymmetric eddy current model of an induction furnaceIMA J. Numer. Anal.30, 654–676.spa
dcterms.references[16] 2002Ci Ciarlet, P. (2002) The Finite Element Method for Elliptic Problems. New York: SIAM.spa
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dcterms.references[21] Gopalakrishnan, J. & Pasciak, J. (2006) The convergence of V-cycle mul tigrid algorithms for axisymmetric Laplace and Maxwell equations, Math. Comp. 75, 1697–1719.spa
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dcterms.references[24] Mercier, B. & Raugel, G. (1982) Resolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en ◊, RAIRO, Anal. Numér. 16, 405–461.spa
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oaire.versionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
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