Geodesic
On monotone and Schwarz alternating methods for nonlinear elliptic PDEs
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 1-15

Voir la notice de l'article provenant de la source Numdam

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.

Classification : 65N55, 65J15
Keywords: 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: Mathematical Modelling and Numerical Analysis },
     pages = {1--15},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {1},
     year = {2001},
     mrnumber = {1811978},
     zbl = {0976.65109},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
PY  - 2001
SP  - 1
EP  - 15
VL  - 35
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_1_0/
LA  - en
ID  - M2AN_2001__35_1_1_0
ER  - 
%0 Journal Article
%A Lui, Shiu-Hong
%T On monotone and Schwarz alternating methods for nonlinear elliptic PDEs
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2001
%P 1-15
%V 35
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_1_0/
%G en
%F M2AN_2001__35_1_1_0
Lui, Shiu-Hong. On monotone and Schwarz alternating methods for nonlinear elliptic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 1, pp. 1-15. http://geodesic.mathdoc.fr/item/M2AN_2001__35_1_1_0/