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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 11, Issue 4


Robust discretization and a posteriori control for strongly oscillating solutions of the stationary Schrödinger equation

Willy Dörfler
  • Institut für Angewandte und Numerische Mathematik 2, Karlsruher Institut für Technologie (KIT), 76128, Karlsruhe, Germany.
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We consider an example of a boundary value problem on an interval where the solution can show strong oscillations. In order to solve such a problem numerically, standard methods require meshes that resolve these oscillations and will thus need a prohibitively large number of unknowns. In our approach we use special problem dependent basis functions in the finite element method and provide an analysis for a priori and a posteriori bounds. In this way we can construct an efficient approximation method for the solution of such boundary value problems.

Keywords: A posteriori error estimates; a priori error estimates; boundary value problems; computable error bounds; exponential fitting; Schrödinger equation

About the article

Received: 2011-06-21

Revised: 2011-09-19

Accepted: 2011-10-21

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 11, Issue 4, Pages 418–440, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2011-0024.

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© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 4.0

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