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

Antonopoulou, Dimitra
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University of Chester
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2015-06-30
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Mathematics
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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.
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
Publisher
EDP Sciences
Journal
ESAIM: M2AN
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URI
http://hdl.handle.net/10034/338552
DOI
10.1051/m2an/2015004
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Type
Article
Language
en
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/
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ISSN
2822-7840
EISSN
2804-7214
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