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

Boulmezaoud, Tahar Zamène

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 1, pp. 109-145.

In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of ${ℝ}^n$. 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.

Classification : 35J, 35J05, 65Jxx, 65Nxx, 65Rxx
Mots clés : unbounded domains, inverted elements method, weighted Sobolev spaces

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