Free Access
| Issue |
ESAIM: M2AN
Volume 49, Number 4, July-August 2015
|
|
|---|---|---|
| Page(s) | 1127 - 1156 | |
| DOI | https://doi.org/10.1051/m2an/2015004 | |
| Published online | 30 June 2015 | |
- L. Abrahamsson and H.O. Kreiss, The initial boundary value problem for the Schrödinger equation. Math. Methods Appl. Sci. 13 (1990a) 385–390. [CrossRef] [Google Scholar]
- L. Abrahamsson and H.O. Kreiss, Boundary conditions for the parabolic equation in a range-dependent duct. J. Acoust. Soc. Amer. 87 (1990b) 2438–2441. [CrossRef] [MathSciNet] [Google Scholar]
- G.D. Akrivis and V.A. Dougalis, Finite difference discretization with variable mesh of the Schrödinger equation in a variable domain. Bull. Greek Math. Soc. 31 (1990) 19–28. [Google Scholar]
- G.D. Akrivis, V.A. Dougalis and G.E. Zouraris, Finite difference schemes for the ‘Parabolic’ Equation in a variable depth environment with a rigid bottom boundary condition. SIAM J. Numer. Anal. 39 (2001) 539-565. [CrossRef] [Google Scholar]
- D.C. Antonopoulou, Theory and numerical analysis of parabolic approximations. Ph.D. thesis (in Greek). University of Athens, Greece (2006). [Google Scholar]
- D.C. Antonopoulou, Galerkin methods for the ‘Parabolic Equation’ Dirichlet problem in a variable 2-D and 3-D topography, Appl. Numer. Math. 67 (2013) 17–34. [CrossRef] [Google Scholar]
- D.C. Antonopoulou and M. Plexousakis, Discontinuous Galerkin methods for the linear Schrödinger equation in noncylindrical domains. Numer. Math. 115 (2010) 585–608. [CrossRef] [MathSciNet] [Google Scholar]
- D.C. Antonopoulou, V.A. Dougalis and G.E. Zouraris, Galerkin methods for parabolic and Schrödinger equations with dynamical boundary conditions and applications to underwater acoustics. SIAM J. Numer. Anal. 47 (2009) 2752–2781. [CrossRef] [Google Scholar]
- D.C. Antonopoulou, G.D. Karali, M. Plexousakis and G.E. Zouraris, Crank–Nicolson finite element discretizations for a two dimensional linear Schrödinger-type equation posed in a noncylindrical domain. Math. Comput. 84 (2015) 1571–1598. [CrossRef] [Google Scholar]
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. In vol. 15 of Texts Appl. Math. Springer-Verlag, New York (1994). [Google Scholar]
- V.A. Dougalis, N.A. Kampanis, F. Sturm, and G.E. Zouraris, Numerical solution of the Parabolic Equation in range-dependent waveguides in Effective Computational Methods for Wave Propagation. Edited by N.A. Kampanis et al. Chapman and Hall/CRC, Boca Raton (2008) 175–207. [Google Scholar]
- M. Ehrhardt, Discrete artificial boundary conditions. Ph.D. thesis, Technische Universität, Berlin (2001). [Google Scholar]
- J. Escher, Quasilinear parabolic systems with dynamical boundary conditions, Commun. Partial. Differ. Eqs. 18 (1993) 1309–1364. [Google Scholar]
- L.C. Evans, Partial Differential Equations. In vol. 19 of Grad. Stud. Math. American Mathematical Society (1998). [Google Scholar]
- F.B. Jensen, W.A. Kuperman, M.B. Porter, H. Schmidt, Computational Ocean Acoustics. AIP Series in Modern Acoustics and Signal Processing. American Institute of Physics, New York (1994). [Google Scholar]
- M.H. Schultz, Spline Analysis. Prentice-Hall (1973). [Google Scholar]
- F. Sturm, Modélisation mathématique et numérique d’ un problème de propagation en acoustique sous-marine: prise en compte d’un environnement variable tridimensionnel. Ph.D. thesis, Université de Toulon et du Var, France (1997). [Google Scholar]
- F.D. Tappert, The parabolic approximation method, in Wave Propagation and Underwater Acoustics, edited by J.B. Keller and J.S. Papadakis. In vol. 70 of Lect. Notes Phys. Springer-Verlag, Berlin (1977) 224-287. [Google Scholar]
- J.L. Vázquez and E. Vitillaro, Heat equation with dynamical boundary conditions of reactive type. Commun. Partial. Differ. Eqs. 33 (2008) 561–612. [Google Scholar]
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