Kornhuber, R. and Podlesny, J. and Yserentant, H.
(2017)
*Direct and Iterative Methods for Numerical Homogenization.*
In:
Domain Decomposition Methods in Science and Engineering.
Lecture Notes in Computational Science and Engineering, XXIII
(116).
SpringerLink, pp. 217-225.
ISBN 978-3-319-52389-7

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Official URL: http://dx.doi.org/10.1007/978-3-319-52389-7_21

## Abstract

Elliptic problems with oscillating coefficients can be approximated up to arbitrary accuracy by using sufficiently fine meshes, i.e., by resolving the fine scale. Well-known multiscale finite elements [5, 9] can be regarded as direct numerical homogenization methods in the sense that they provide approximations of the corresponding (unfeasibly) large linear systems by much smaller systems while preserving the fine-grid discretization accuracy (model reduction). As an alternative, we present iterative numerical homogenization methods that provide approximations up to fine-grid discretization accuracy and discuss differences and commonalities.

Item Type: | Book Section |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 1792 |

Deposited By: | Ulrike Eickers |

Deposited On: | 15 Feb 2016 12:23 |

Last Modified: | 22 Sep 2017 11:36 |

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