Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain
AffiliationUniversity of Chester
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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.
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/S0025-5718-2014-02900-1
JournalMathematics of Computation
DescriptionFirst published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical Society
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