Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain

Hdl Handle:
http://hdl.handle.net/10034/561316
Title:
Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain
Authors:
Antonopoulou, Dimitra; Karali, Georgia D.; Plexousakis, Michael; Zouraris, Georgios
Abstract:
Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundary-value problem for a general Schr¨odinger-type equation posed on a two space-dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain, and we approximate its solution by a Crank–Nicolson finite element method. For the proposed numerical method, we derive an optimal order error estimate in the L2 norm, and to support the error analysis we prove a global elliptic regularity theorem for complex elliptic boundary value problems with mixed boundary conditions. Results from numerical experiments are presented which verify the optimal order of convergence of the method.
Affiliation:
University of Chester
Citation:
Antonopoulou, D. C., Karali, G. D., Plexousakis, M. & Zouraris, G. E. (2014). Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain. Mathematics of Computation, 84 (294), 1571-1598. DOI: 10.1090/S0025-5718-2014-02900-1
Publisher:
AMS
Journal:
Mathematics of Computation
Publication Date:
5-Nov-2014
URI:
http://hdl.handle.net/10034/561316
Additional Links:
http://www.ams.org/journals/mcom/2015-84-294/S0025-5718-2014-02900-1/
Type:
Article
Language:
en
Description:
First published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical Society
ISSN:
0025-5718
EISSN:
1088-6842
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonopoulou, Dimitraen
dc.contributor.authorKarali, Georgia D.en
dc.contributor.authorPlexousakis, Michaelen
dc.contributor.authorZouraris, Georgiosen
dc.date.accessioned2015-07-31T14:19:02Zen
dc.date.available2015-07-31T14:19:02Zen
dc.date.issued2014-11-05en
dc.identifier.citationAntonopoulou, D. C., Karali, G. D., Plexousakis, M. & Zouraris, G. E. (2014). Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain. Mathematics of Computation, 84 (294), 1571-1598. DOI: 10.1090/S0025-5718-2014-02900-1en
dc.identifier.issn0025-5718en
dc.identifier.urihttp://hdl.handle.net/10034/561316en
dc.descriptionFirst published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical Societyen
dc.description.abstractMotivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundary-value problem for a general Schr¨odinger-type equation posed on a two space-dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain, and we approximate its solution by a Crank–Nicolson finite element method. For the proposed numerical method, we derive an optimal order error estimate in the L2 norm, and to support the error analysis we prove a global elliptic regularity theorem for complex elliptic boundary value problems with mixed boundary conditions. Results from numerical experiments are presented which verify the optimal order of convergence of the method.en
dc.language.isoenen
dc.publisherAMSen
dc.relation.urlhttp://www.ams.org/journals/mcom/2015-84-294/S0025-5718-2014-02900-1/en
dc.titleCrank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domainen
dc.typeArticleen
dc.identifier.eissn1088-6842en
dc.contributor.departmentUniversity of Chesteren
dc.identifier.journalMathematics of Computationen
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