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Numerische Mathematik

, Volume 115, Issue 4, pp 585–608 | Cite as

Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains

  • D. C. Antonopoulou
  • M. Plexousakis
Article

Abstract

The convergence of a discontinuous Galerkin method for the linear Schrödinger equation in non-cylindrical domains of \({\mathbb{R}^m}\), m ≥ 1, is analyzed in this paper. We show the existence of the resulting approximations and prove stability and error estimates in finite element spaces of general type. When m = 1 the resulting problem is related to the standard narrow angle ‘parabolic’ approximation of the Helmholtz equation, as it appears in underwater acoustics. In this case we investigate theoretically and numerically the order of convergence using finite element spaces of piecewise polynomial functions.

Mathematics Subject Classification (2000)

65M12 65M15 65M60 

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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of CreteHeraklionGreece
  2. 2.Institute of Applied and Computational MathematicsFO.R.T.H.HeraklionGreece

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