Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions

Hdl Handle:
http://hdl.handle.net/10034/338552
Title:
Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions
Authors:
Antonopoulou, Dimitra
Abstract:
In this paper, we consider a two-dimensional Schodinger-type equation with a dynamical boundary condition. This model describes the long-range sound propagation in naval environments of variable rigid bottom topography. Our choice for a regular enough finite element approximation is motivated by the dynamical condition and therefore, consists of a cubic splines implicit Galerkin method in space. Furthermore, we apply a Crank-Nicolson time stepping for the evolutionary variable. We prove existence and stability of the semidiscrete and fully discrete solution.
Affiliation:
University of Chester
Citation:
Antonopoulou, D. (2015). Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions. ESAIM: M2AN - Mathematical Modelling and Numerical Analysis, (49)4, 1127-1156. DOI: 10.1051/m2an/2015004
Publisher:
EDP Sciences / SMAI
Journal:
ESAIM M2AN - Mathematical Modelling and Numerical Analysis
Publication Date:
30-Jun-2015
URI:
http://hdl.handle.net/10034/338552
DOI:
10.1051/m2an/2015004
Additional Links:
http://www.esaim-m2an.org/; http://www.esaim-m2an.org/articles/m2an/abs/2015/04/m2an150004-s/m2an150004-s.html
Type:
Article
Language:
en
Description:
This is the author's PDF version of an article published in ESAIM: Mathematical modelling and numerical analysis© 2015. The definitive version is available at http://www.esaim-m2an.org/
ISSN:
0764-583X; 1290-3841
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonopoulou, Dimitraen
dc.date.accessioned2015-01-19T13:11:59Zen
dc.date.available2015-01-19T13:11:59Zen
dc.date.issued2015-06-30en
dc.identifier.citationAntonopoulou, D. (2015). Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions. ESAIM: M2AN - Mathematical Modelling and Numerical Analysis, (49)4, 1127-1156. DOI: 10.1051/m2an/2015004en
dc.identifier.issn0764-583Xen
dc.identifier.issn1290-3841en
dc.identifier.doi10.1051/m2an/2015004en
dc.identifier.urihttp://hdl.handle.net/10034/338552en
dc.descriptionThis is the author's PDF version of an article published in ESAIM: Mathematical modelling and numerical analysis© 2015. The definitive version is available at http://www.esaim-m2an.org/en
dc.description.abstractIn this paper, we consider a two-dimensional Schodinger-type equation with a dynamical boundary condition. This model describes the long-range sound propagation in naval environments of variable rigid bottom topography. Our choice for a regular enough finite element approximation is motivated by the dynamical condition and therefore, consists of a cubic splines implicit Galerkin method in space. Furthermore, we apply a Crank-Nicolson time stepping for the evolutionary variable. We prove existence and stability of the semidiscrete and fully discrete solution.en
dc.language.isoenen
dc.publisherEDP Sciences / SMAIen
dc.relation.urlhttp://www.esaim-m2an.org/en
dc.relation.urlhttp://www.esaim-m2an.org/articles/m2an/abs/2015/04/m2an150004-s/m2an150004-s.htmlen
dc.subject2-D Schrodinger equationen
dc.subjectfinite element methodsen
dc.subjecterror estimatesen
dc.subjectnoncylindrical domainen
dc.subjectNeumann boundary conditionen
dc.subjectcubic splinesen
dc.subjectCrank-Nicolson time steppingen
dc.subjectdynamical boundary conditionen
dc.subjectunderwater acousticsen
dc.titleGalerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensionsen
dc.typeArticleen
dc.contributor.departmentUniversity of Chesteren
dc.identifier.journalESAIM M2AN - Mathematical Modelling and Numerical Analysisen
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