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Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain
Antonopoulou, Dimitra Karali, Georgia D. Plexousakis, Michael Zouraris, Georgios
Antonopoulou, Dimitra
Karali, Georgia D.
Plexousakis, Michael
Zouraris, Georgios
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2014-11-05
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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.
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
American Mathematical Society
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Mathematics of Computation
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Article
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en
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First published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical Society
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ISSN
0025-5718
EISSN
1088-6842