Inverted finite elements: a new method for solving elliptic problems in unbounded domains
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. firstname.lastname@example.org
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