| Issue |
ESAIM: M2AN
Volume 39, Number 1, January-February 2005
|
|
|---|---|---|
| Page(s) | 109 - 145 | |
| DOI | https://doi.org/10.1051/m2an:2005001 | |
| Published online | 15 March 2005 | |
Inverted finite elements: a new method for solving elliptic problems in unbounded domains
1
Laboratoire de Mathématiques,
Université de Versailles Saint-Quentin en Yvelines (UVSQ),
45 avenue des États-Unis, Bâtiment Fermat,
78035 Versailles, France.
2
Laboratoire Jacques-Louis Lions,
Université Paris VI, BC187, 75252 Paris
Cedex, France.
boulmeza@math.uvsq.fr
Received:
15
December
2003
In this paper, we propose a new numerical method for solving
elliptic equations in unbounded regions of 
. 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.
Mathematics Subject Classification: 35J / 35J05 / 65Jxx / 65Nxx / 65Rxx
Key words: Unbounded domains / inverted elements method / weighted Sobolev spaces.
© EDP Sciences, SMAI, 2005
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