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Inverted finite elements: a new methodfor solving elliptic problems in unbounded domains

Published online by Cambridge University Press:  15 March 2005

Tahar Zamène Boulmezaoud
Tahar Zamène Boulmezaoud*
Affiliation:
Laboratoire de Mathématiques, Université de Versailles Saint-Quentin en Yvelines (UVSQ), 45 avenue des États-Unis, Bâtiment Fermat, 78035 Versailles, France. Laboratoire Jacques-Louis Lions, Université Paris VI, BC187, 75252 Paris Cedex, France. boulmeza@math.uvsq.fr
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Abstract

In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of ${\mathbb{R}}^n$. The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.

Keywords

Unbounded domainsinverted elements methodweighted Sobolev spaces.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 1 , January 2005 , pp. 109 - 145
Copyright
© EDP Sciences, SMAI, 2005

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