Antonopoulou, DimitraKarali, Georgia D.Plexousakis, MichaelZouraris, Georgios2015-07-312015-07-312014-11-05Antonopoulou, 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/S0025-5718-2014-02900-10025-5718http://hdl.handle.net/10034/561316First published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical SocietyMotivated 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.enArticle1088-6842Mathematics of Computation