Inverted finite elements : a new method for solving elliptic problems in unbounded domains
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 1, p. 109-145

In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of 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.

DOI : https://doi.org/10.1051/m2an:2005001
Classification:  35J,  35J05,  65Jxx,  65Nxx,  65Rxx
Keywords: unbounded domains, inverted elements method, weighted Sobolev spaces
@article{M2AN_2005__39_1_109_0,
     author = {Boulmezaoud, Tahar Zam\`ene},
     title = {Inverted finite elements : a new method for solving elliptic problems in unbounded domains},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {1},
     year = {2005},
     pages = {109-145},
     doi = {10.1051/m2an:2005001},
     zbl = {1078.65102},
     mrnumber = {2136202},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_1_109_0}
}
Boulmezaoud, Tahar Zamène. Inverted finite elements : a new method for solving elliptic problems in unbounded domains. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 1, pp. 109-145. doi : 10.1051/m2an:2005001. http://www.numdam.org/item/M2AN_2005__39_1_109_0/

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