Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions
| dc.contributor.author | Antonopoulou, Dimitra | * |
| dc.date.accessioned | 2015-01-19T13:11:59Z | |
| dc.date.available | 2015-01-19T13:11:59Z | |
| dc.date.issued | 2015-06-30 | |
| dc.identifier.citation | Antonopoulou, D. (2015). Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions. ESAIM: M2AN, (49)4, 1127-1156. DOI: 10.1051/m2an/2015004 | en |
| dc.identifier.issn | 2822-7840 | en |
| dc.identifier.doi | 10.1051/m2an/2015004 | |
| dc.identifier.uri | http://hdl.handle.net/10034/338552 | |
| dc.description | This is the author's PDF version of an article published in ESAIM: M2AN© 2015. The definitive version is available at http://www.esaim-m2an.org/ | en |
| dc.description.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. | |
| dc.language.iso | en | en |
| dc.publisher | EDP Sciences | en |
| dc.relation.url | http://www.esaim-m2an.org/ | en |
| dc.relation.url | http://www.esaim-m2an.org/articles/m2an/abs/2015/04/m2an150004-s/m2an150004-s.html | en |
| dc.subject | 2-D Schrodinger equation | en |
| dc.subject | finite element methods | en |
| dc.subject | error estimates | en |
| dc.subject | noncylindrical domain | en |
| dc.subject | Neumann boundary condition | en |
| dc.subject | cubic splines | en |
| dc.subject | Crank-Nicolson time stepping | en |
| dc.subject | dynamical boundary condition | en |
| dc.subject | underwater acoustics | en |
| dc.title | Galerkin methods for a Schroedinger-type equation with a dynamical boundary condition in two dimensions | en |
| dc.type | Article | en |
| dc.identifier.eissn | 2804-7214 | |
| dc.contributor.department | University of Chester | en |
| dc.identifier.journal | ESAIM: M2AN | |
| html.description.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. | |
| rioxxterms.publicationdate | 2015-06-30 |
