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| HAL: hal-00694017, version 1 |
| arXiv: 1205.0331 |
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| Non-consistent approximations of self-adjoint eigenproblems: Application to the supercell method |
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| Eric Cancès 1, 2Virginie Ehrlacher 1, 2 |
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| (2012-05-02) |
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| In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eigenvalues laying in spectral gaps. We first provide a priori error estimates on the eigenvalues and eigenvectors in the absence of spectral pollution. We then show that the supercell method for perturbed periodic Schrödinger operators falls into the scope of our study. We prove that this method is spectral pollution free, and we derive optimal convergence rates for the planewave discretization method, taking numerical integration errors into account. Some numerical illustrations are provided. |
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| 1: | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| 2: | MICMAC (INRIA Paris - Rocquencourt) |
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Ecole des Ponts ParisTech – INRIA |
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| 3: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| Subject | : | Mathematics/Functional Analysis |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1205.0331 |
| hal-00694017, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00694017 | |
| oai:hal.archives-ouvertes.fr:hal-00694017 | |
| From: Virginie Ehrlacher | |
| Submitted on: Thursday, 3 May 2012 13:00:55 | |
| Updated on: Thursday, 3 May 2012 13:01:35 | |
