The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method of subsolutions and supersolutions) are given. In particular, an additive Schwarz method for scalar as well as some coupled nonlinear PDEs are shown to converge for finitely many subdomains. These results are applicable to several models in population biology.
Mots-clés : domain decomposition, nonlinear elliptic PDE, Schwarz alternating method, monotone methods, subsolution, supersolution
@article{M2AN_2001__35_1_1_0,
author = {Lui, Shiu-Hong},
title = {On monotone and {Schwarz} alternating methods for nonlinear elliptic {PDEs}},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1--15},
publisher = {EDP-Sciences},
volume = {35},
number = {1},
year = {2001},
mrnumber = {1811978},
zbl = {0976.65109},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_1_1_0/}
}
TY - JOUR AU - Lui, Shiu-Hong TI - On monotone and Schwarz alternating methods for nonlinear elliptic PDEs JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 1 EP - 15 VL - 35 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_1_1_0/ LA - en ID - M2AN_2001__35_1_1_0 ER -
Lui, Shiu-Hong. On monotone and Schwarz alternating methods for nonlinear elliptic PDEs. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 1, pp. 1-15. http://www.numdam.org/item/M2AN_2001__35_1_1_0/
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