A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation

The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for...

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Autores:
Ruiz Vera, Jorge Mauricio
Mantilla Prada, Ignacio
Tipo de recurso:
Fecha de publicación:
2013
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/14412
Acceso en línea:
http://hdl.handle.net/10784/14412
Palabra clave:
Finite Elements
Nonlinear Evolution Equations
Semiconductors
Elementos Finitos
Ecuaciones De Evolución No Lineal
Semiconductores
Rights
License
Copyright (c) 2013 Jorge Mauricio Ruiz Vera, Ignacio Mantilla Prada
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spelling Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2013-03-222019-11-22T17:02:39Z2013-03-222019-11-22T17:02:39Z2256-43141794-9165http://hdl.handle.net/10784/1441210.17230/ingciecia.9.17.5The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS) es un cuarto orden en la ecuación de evolución no lineal del espacio. Esta ecuación surge en el estudio de las fluctuaciones de la interfaz en los sistemas de espín y el modelado cuántico de semiconductores. En este artículo, presentamos una discrtización positiva de elementos finitos de preservación para un enfoque de ecuaciones acopladas a la ecuación DLSS. Usando la información disponible sobre los fenómenos físicos, podemos establecer las condiciones de contorno correspondientes para el sistema acoplado. Probamos la existencia de una solución discreta global en el tiempo mediante un argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta una prueba de orden de convergencia del esquema de discretización propuesto.application/pdfengUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1737http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1737Copyright (c) 2013 Jorge Mauricio Ruiz Vera, Ignacio Mantilla PradaAcceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 9, No 17 (2013)A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equationUn esquema de elementos finitos completamente discreto para la ecuación de Derrida-Lebowitz-Speer-Spohnarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Finite ElementsNonlinear Evolution EquationsSemiconductorsElementos FinitosEcuaciones De Evolución No LinealSemiconductoresRuiz Vera, Jorge MauricioMantilla Prada, IgnacioUniversidad Nacional de ColombiaIngeniería y Ciencia91797110ing.cienc.ORIGINALdocument (7).pdfdocument (7).pdfTexto completo PDFapplication/pdf755287https://repository.eafit.edu.co/bitstreams/b5e32b61-4428-4862-95ec-2c3853803085/downloadf7bd1c68b1d8dea253b013916fe62fa9MD51THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/1055f8a4-c664-4eee-9fc0-bead79444a9a/downloadda9b21a5c7e00c7f1127cef8e97035e0MD5210784/14412oai:repository.eafit.edu.co:10784/144122020-02-16 11:38:39.674open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
dc.title.spa.fl_str_mv Un esquema de elementos finitos completamente discreto para la ecuación de Derrida-Lebowitz-Speer-Spohn
title A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
spellingShingle A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
Finite Elements
Nonlinear Evolution Equations
Semiconductors
Elementos Finitos
Ecuaciones De Evolución No Lineal
Semiconductores
title_short A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
title_full A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
title_fullStr A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
title_full_unstemmed A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
title_sort A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation
dc.creator.fl_str_mv Ruiz Vera, Jorge Mauricio
Mantilla Prada, Ignacio
dc.contributor.author.spa.fl_str_mv Ruiz Vera, Jorge Mauricio
Mantilla Prada, Ignacio
dc.contributor.affiliation.spa.fl_str_mv Universidad Nacional de Colombia
dc.subject.keyword.eng.fl_str_mv Finite Elements
Nonlinear Evolution Equations
Semiconductors
topic Finite Elements
Nonlinear Evolution Equations
Semiconductors
Elementos Finitos
Ecuaciones De Evolución No Lineal
Semiconductores
dc.subject.keyword.spa.fl_str_mv Elementos Finitos
Ecuaciones De Evolución No Lineal
Semiconductores
description The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.
publishDate 2013
dc.date.issued.none.fl_str_mv 2013-03-22
dc.date.available.none.fl_str_mv 2019-11-22T17:02:39Z
dc.date.accessioned.none.fl_str_mv 2019-11-22T17:02:39Z
dc.date.none.fl_str_mv 2013-03-22
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
publishedVersion
info:eu-repo/semantics/publishedVersion
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http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.local.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 2256-4314
1794-9165
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/14412
dc.identifier.doi.none.fl_str_mv 10.17230/ingciecia.9.17.5
identifier_str_mv 2256-4314
1794-9165
10.17230/ingciecia.9.17.5
url http://hdl.handle.net/10784/14412
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.isversionof.none.fl_str_mv http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1737
dc.relation.uri.none.fl_str_mv http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/1737
dc.rights.eng.fl_str_mv Copyright (c) 2013 Jorge Mauricio Ruiz Vera, Ignacio Mantilla Prada
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.local.spa.fl_str_mv Acceso abierto
rights_invalid_str_mv Copyright (c) 2013 Jorge Mauricio Ruiz Vera, Ignacio Mantilla Prada
Acceso abierto
http://purl.org/coar/access_right/c_abf2
dc.format.none.fl_str_mv application/pdf
dc.coverage.spatial.eng.fl_str_mv Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees
dc.publisher.spa.fl_str_mv Universidad EAFIT
dc.source.none.fl_str_mv instname:Universidad EAFIT
reponame:Repositorio Institucional Universidad EAFIT
dc.source.spa.fl_str_mv Ingeniería y Ciencia; Vol 9, No 17 (2013)
instname_str Universidad EAFIT
institution Universidad EAFIT
reponame_str Repositorio Institucional Universidad EAFIT
collection Repositorio Institucional Universidad EAFIT
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