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

Tahar Zamène Boulmezaoud

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 1, page 109-145
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Boulmezaoud, Tahar Zamène. "Inverted finite elements: a new method for solving elliptic problems in unbounded domains." ESAIM: Mathematical Modelling and Numerical Analysis 39.1 (2010): 109-145. <http://eudml.org/doc/194253>.

@article{Boulmezaoud2010,
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. },
author = {Boulmezaoud, Tahar Zamène},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Unbounded domains; inverted elements method; weighted Sobolev spaces. ; finite elements; elliptic problems; convergence; weighted spaces; unbounded region; numerical experiments},
language = {eng},
month = {3},
number = {1},
pages = {109-145},
publisher = {EDP Sciences},
title = {Inverted finite elements: a new method for solving elliptic problems in unbounded domains},
url = {http://eudml.org/doc/194253},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Boulmezaoud, Tahar Zamène
TI - Inverted finite elements: a new method for solving elliptic problems in unbounded domains
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 1
SP - 109
EP - 145
AB - 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.
LA - eng
KW - Unbounded domains; inverted elements method; weighted Sobolev spaces. ; finite elements; elliptic problems; convergence; weighted spaces; unbounded region; numerical experiments
UR - http://eudml.org/doc/194253
ER -

References

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