A new technique for analysing problems which extend to infinity using elements is presented. A typical situation is that of the unbounded surface wave problems, either in two or three dimensions. The strategy is to discretize the inner domain in the standard finite element manner and to discretize the outer domain which extends to infinity with special infinite elements, for these elements are here suggested a series of shape functions analogous to Lagrange polynomials, but including an exponential decay. These shape functions are applied to an illustrative example which shows the success of the method.
@article{RLINA_1980_8_69_6_380_0,
author = {Gianmaria Donida and Luisa Tabusso},
title = {Discretizzazione di domini infiniti (elementi infiniti). Nota II},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {68},
year = {1980},
pages = {380-385},
zbl = {0491.76027},
mrnumber = {0690305},
language = {it},
url = {http://dml.mathdoc.fr/item/RLINA_1980_8_69_6_380_0}
}
Donida, Gianmaria; Tabusso, Luisa. Discretizzazione di domini infiniti (elementi infiniti). Nota II. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 68 (1980) pp. 380-385. http://gdmltest.u-ga.fr/item/RLINA_1980_8_69_6_380_0/
[1] (1977) - Infinite Elements, «International Journal for Numerical Methods in Engineering», 11, 53-64. | Zbl 0362.65093
[2] e (1970) - Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables, Ed. Milton, New York.
[3] (1971) - The Finite Element Method in Engineering Science, McGraw-Hill, London. | Zbl 0237.73071
[4] e (1974) - Computationally Efficient Finite Element Analysis of Viscous Flow Problems, In «Computational Methods in Non Linear Mechanics», Ed. and Al., Texas Institute for Computational Mechanics. | Zbl 0309.76028